output.var = params$output.var
transform.abs = FALSE
log.pred = params$log.pred
norm.pred = FALSE
algo.forward.caret = params$algo.forward.caret
algo.backward.caret = params$algo.backward.caret
algo.stepwise.caret = params$algo.stepwise.caret
algo.LASSO.caret = params$algo.LASSO.caret
algo.LARS.caret = params$algo.LARS.caret
message("Parameters used for training/prediction: ")
## Parameters used for training/prediction:
str(params)
## List of 7
## $ output.var : chr "y3"
## $ log.pred : logi TRUE
## $ algo.forward.caret : logi TRUE
## $ algo.backward.caret: logi TRUE
## $ algo.stepwise.caret: logi TRUE
## $ algo.LASSO.caret : logi TRUE
## $ algo.LARS.caret : logi TRUE
# Setup Labels
output.var.tr = if (log.pred == TRUE) paste0(output.var,'.log') else output.var.tr = output.var
feat = read.csv('../../Data/features_highprec.csv')
labels = read.csv('../../Data/labels.csv')
predictors = names(dplyr::select(feat,-JobName))
data.ori = inner_join(feat,labels,by='JobName')
#data.ori = inner_join(feat,select_at(labels,c('JobName',output.var)),by='JobName')
cc = complete.cases(data.ori)
data.notComplete = data.ori[! cc,]
data = data.ori[cc,] %>% select_at(c(predictors,output.var,'JobName'))
message('Original cases: ',nrow(data.ori))
## Original cases: 10000
message('Non-Complete cases: ',nrow(data.notComplete))
## Non-Complete cases: 3020
message('Complete cases: ',nrow(data))
## Complete cases: 6980
summary(dplyr::select_at(data,c('JobName',output.var)))
## JobName y3
## Job_00001: 1 Min. : 95.91
## Job_00002: 1 1st Qu.:118.29
## Job_00003: 1 Median :124.03
## Job_00004: 1 Mean :125.40
## Job_00007: 1 3rd Qu.:131.06
## Job_00008: 1 Max. :193.73
## (Other) :6974
The Output Variable y3 shows right skewness, so will proceed with a log transformation
df=gather(select_at(data,output.var))
ggplot(df, aes(x=value)) +
geom_histogram(aes(y=..density..),bins = 50,fill='light blue') +
geom_density()
#stat_function(fun = dnorm, n = 100, args = list(mean = mean(df$value), sd = sd(df$value)))
ggplot(gather(select_at(data,output.var)), aes(sample=value)) +
stat_qq() +
facet_wrap(~key, scales = 'free',ncol=4)
if(log.pred==TRUE) data[[output.var.tr]] = log(data[[output.var]],10) else
data[[output.var.tr]] = data[[output.var]]
df=gather(select_at(data,c(output.var,output.var.tr)))
ggplot(df, aes(value)) +
geom_histogram(aes(y=..density..),bins = 50,fill='light blue') +
geom_density() +
# stat_function(fun = dnorm, n = 100, args = list(mean = mean(df$value), sd = sd(df$value)))
facet_wrap(~key, scales = 'free',ncol=2)
ggplot(gather(select_at(data,c(output.var,output.var.tr))), aes(sample=value)) +
stat_qq() +
facet_wrap(~key, scales = 'free',ncol=4)
Normalization of y3 using bestNormalize package. (suggested orderNorm) This is cool, but I think is too far for the objective of the project
t=bestNormalize::bestNormalize(data[[output.var]])
t
## Best Normalizing transformation with 6980 Observations
## Estimated Normality Statistics (Pearson P / df, lower => more normal):
## - No transform: 2.9625
## - Box-Cox: 1.4152
## - Log_b(x+a): 2.0249
## - sqrt(x+a): 2.4466
## - exp(x): 749.2827
## - arcsinh(x): 2.0256
## - Yeo-Johnson: 1.1673
## - orderNorm: 1.1755
## Estimation method: Out-of-sample via CV with 10 folds and 5 repeats
##
## Based off these, bestNormalize chose:
## Standardized Yeo-Johnson Transformation with 6980 nonmissing obs.:
## Estimated statistics:
## - lambda = -1.998639
## - mean (before standardization) = 0.5003083
## - sd (before standardization) = 5.108542e-06
qqnorm(data[[output.var]])
qqnorm(predict(t))
orderNorm() is a rank-based procedure by which the values of a vector are mapped to their percentile, which is then mapped to the same percentile of the normal distribution. Without the presence of ties, this essentially guarantees that the transformation leads to a uniform distribution
All predictors show a Fat-Tail situation, where the two tails are very tall, and a low distribution around the mean. The orderNorm transformation can help (see [Best Normalizator] section)
Histograms
cols = c('x11','x18','stat98','x7','stat110')
df=gather(select_at(data,cols))
ggplot(df, aes(value)) +
geom_histogram(aes(y=..density..),bins = 50,fill='light blue') +
geom_density() +
# stat_function(fun = dnorm, n = 100, args = list(mean = mean(df$value), sd = sd(df$value)))
facet_wrap(~key, scales = 'free',ncol=3)
# ggplot(gather(select_at(data,cols)), aes(sample=value)) +
# stat_qq()+
# facet_wrap(~key, scales = 'free',ncol=2)
lapply(select_at(data,cols),summary)
## $x11
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 9.000e-08 9.494e-08 1.001e-07 1.001e-07 1.052e-07 1.100e-07
##
## $x18
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.500 3.147 4.769 4.772 6.418 7.999
##
## $stat98
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -2.998619 -1.551882 -0.015993 -0.005946 1.528405 2.999499
##
## $x7
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.700 1.266 1.854 1.852 2.446 3.000
##
## $stat110
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -2.999543 -1.496865 -0.002193 -0.004129 1.504273 2.999563
Scatter plot vs. output variable **y3.log
d = gather(dplyr::select_at(data,c(cols,output.var.tr)),key=target,value=value,-!!output.var.tr)
ggplot(data=d, aes_string(x='value',y=output.var.tr)) +
geom_point(color='light green',alpha=0.5) +
geom_smooth() +
facet_wrap(~target, scales = 'free',ncol=3)
## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
All indicators have a strong indication of Fat-Tails
df=gather(select_at(data,predictors))
ggplot(df, aes(value)) +
geom_histogram(aes(y=..density..),bins = 50,fill='light blue') +
geom_density() +
# stat_function(fun = dnorm, n = 100, args = list(mean = mean(df$value), sd = sd(df$value)))
facet_wrap(~key, scales = 'free',ncol=4)
#chart.Correlation(select(data,-JobName), pch=21)
t=as.data.frame(round(cor(dplyr::select(data,-one_of(output.var.tr,'JobName'))
,select_at(data,output.var.tr)),4)) %>%
rownames_to_column(var='variable') %>% filter(variable != !!output.var) %>% arrange(-y3.log)
#DT::datatable(t)
message("Top Positive")
## Top Positive
kable(head(arrange(t,desc(y3.log)),20))
| variable | y3.log |
|---|---|
| x18 | 0.3120 |
| x7 | 0.2091 |
| stat98 | 0.1784 |
| x9 | 0.1127 |
| x17 | 0.0611 |
| x16 | 0.0489 |
| x10 | 0.0472 |
| x21 | 0.0412 |
| x11 | 0.0322 |
| x8 | 0.0318 |
| stat156 | 0.0287 |
| stat23 | 0.0234 |
| stat100 | 0.0206 |
| stat144 | 0.0203 |
| stat59 | 0.0202 |
| stat60 | 0.0199 |
| stat195 | 0.0199 |
| stat141 | 0.0194 |
| stat73 | 0.0192 |
| stat197 | 0.0185 |
message("Top Negative")
## Top Negative
kable(head(arrange(t,y3.log),20))
| variable | y3.log |
|---|---|
| stat110 | -0.1594 |
| x4 | -0.0603 |
| stat13 | -0.0345 |
| stat41 | -0.0345 |
| stat14 | -0.0317 |
| stat149 | -0.0309 |
| stat113 | -0.0279 |
| stat4 | -0.0248 |
| stat106 | -0.0236 |
| stat146 | -0.0236 |
| stat186 | -0.0217 |
| stat91 | -0.0210 |
| stat214 | -0.0209 |
| stat5 | -0.0207 |
| stat22 | -0.0202 |
| stat39 | -0.0202 |
| stat175 | -0.0194 |
| stat187 | -0.0193 |
| stat128 | -0.0192 |
| stat37 | -0.0191 |
#chart.Correlation(select(data,-JobName), pch=21)
t=as.data.frame(round(cor(dplyr::select(data,-one_of('JobName'))),4))
#DT::datatable(t,options=list(scrollX=T))
message("Showing only 10 variables")
## Showing only 10 variables
kable(t[1:10,1:10])
| x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | x9 | x10 | |
|---|---|---|---|---|---|---|---|---|---|---|
| x1 | 1.0000 | 0.0034 | -0.0028 | 0.0085 | 0.0068 | 0.0159 | 0.0264 | -0.0012 | 0.0142 | 0.0013 |
| x2 | 0.0034 | 1.0000 | -0.0057 | 0.0004 | -0.0094 | -0.0101 | 0.0089 | 0.0078 | 0.0049 | -0.0214 |
| x3 | -0.0028 | -0.0057 | 1.0000 | 0.0029 | 0.0046 | 0.0006 | -0.0105 | -0.0002 | 0.0167 | -0.0137 |
| x4 | 0.0085 | 0.0004 | 0.0029 | 1.0000 | -0.0059 | 0.0104 | 0.0098 | 0.0053 | 0.0061 | -0.0023 |
| x5 | 0.0068 | -0.0094 | 0.0046 | -0.0059 | 1.0000 | 0.0016 | -0.0027 | 0.0081 | 0.0259 | -0.0081 |
| x6 | 0.0159 | -0.0101 | 0.0006 | 0.0104 | 0.0016 | 1.0000 | 0.0200 | -0.0157 | 0.0117 | -0.0072 |
| x7 | 0.0264 | 0.0089 | -0.0105 | 0.0098 | -0.0027 | 0.0200 | 1.0000 | -0.0018 | -0.0069 | -0.0221 |
| x8 | -0.0012 | 0.0078 | -0.0002 | 0.0053 | 0.0081 | -0.0157 | -0.0018 | 1.0000 | 0.0142 | -0.0004 |
| x9 | 0.0142 | 0.0049 | 0.0167 | 0.0061 | 0.0259 | 0.0117 | -0.0069 | 0.0142 | 1.0000 | 0.0149 |
| x10 | 0.0013 | -0.0214 | -0.0137 | -0.0023 | -0.0081 | -0.0072 | -0.0221 | -0.0004 | 0.0149 | 1.0000 |
Scatter plots with all predictors and the output variable (y3.log)
d = gather(dplyr::select_at(data,c(predictors,output.var.tr)),key=target,value=value,-!!output.var.tr)
ggplot(data=d, aes_string(x='value',y=output.var.tr)) +
geom_point(color='light blue',alpha=0.5) +
geom_smooth() +
facet_wrap(~target, scales = 'free',ncol=4)
## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
No Multicollinearity among predictors
Showing Top predictor by VIF Value
vifDF = usdm::vif(select_at(data,predictors)) %>% arrange(desc(VIF))
head(vifDF,15)
## Variables VIF
## 1 stat200 1.064425
## 2 stat105 1.062772
## 3 stat129 1.060113
## 4 x22 1.059883
## 5 stat186 1.059724
## 6 stat2 1.059350
## 7 stat38 1.059264
## 8 stat124 1.059115
## 9 stat52 1.058905
## 10 stat72 1.058726
## 11 x10 1.058718
## 12 stat46 1.058439
## 13 stat32 1.058189
## 14 stat163 1.058128
## 15 stat20 1.057925
data.tr=data %>%
mutate(x18.sqrt = sqrt(x18))
cols=c('x18','x18.sqrt')
# ggplot(gather(select_at(data.tr,cols)), aes(value)) +
# geom_histogram(aes(y=..density..),bins = 50,fill='light blue') +
# geom_density() +
# facet_wrap(~key, scales = 'free',ncol=4)
d = gather(dplyr::select_at(data.tr,c(cols,output.var.tr)),key=target,value=value,-!!output.var.tr)
ggplot(data=d, aes_string(x='value',y=output.var.tr)) +
geom_point(color='light blue',alpha=0.5) +
geom_smooth() +
facet_wrap(~target, scales = 'free',ncol=4)
## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
#removing unwanted variables
data.tr=data.tr %>%
dplyr::select_at(names(data.tr)[! names(data.tr) %in% c('x18','y3','JobName')])
data=data.tr
label.names=output.var.tr
data = data[sample(nrow(data)),] # randomly shuffle data
split = sample.split(data[,label.names], SplitRatio = 0.8)
data.train = subset(data, split == TRUE)
data.test = subset(data, split == FALSE)
plot.diagnostics <- function(model, train) {
plot(model)
residuals = resid(model) # Plotted above in plot(lm.out)
r.standard = rstandard(model)
r.student = rstudent(model)
df = data.frame(x=predict(model,train),y=r.student)
p=ggplot(data=df,aes(x=x,y=y)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
geom_hline(yintercept = c(-2,0,2),size=1)+
ylab("Student Residuals") +
xlab("Predicted Values")+
ggtitle("Standardized Residual Plot")
plot(p)
# df = data.frame(x=predict(model,train),y=r.standard)
# p=ggplot(data=df,aes(x=x,y=y)) +
# geom_point(color='blue',alpha=0.5,shape=20,size=2) +
# geom_hline(yintercept = c(-2,0,2),size=1)+
# ylab("Standardized Residuals") +
# xlab("Predicted Values")+
# ggtitle("Student Residual Plot")
# plot(p)
# Histogram
df=data.frame(r.student)
p=ggplot(data=df,aes(r.student)) +
geom_histogram(aes(y=..density..),bins = 50,fill='blue',alpha=0.6) +
stat_function(fun = dnorm, n = 100, args = list(mean = 0, sd = 1)) +
ylab("Density")+
xlab("Studentized Residuals")+
ggtitle("Distribution of Studentized Residuals")
plot(p)
# http://www.stat.columbia.edu/~martin/W2024/R7.pdf
# Influential plots
inf.meas = influence.measures(model)
# print (summary(inf.meas)) # too much data
# Leverage plot
lev = hat(model.matrix(model))
df=tibble::rownames_to_column(as.data.frame(lev),'id')
p=ggplot(data=df,aes(x=as.numeric(id),y=lev)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
ylab('Leverage - check') +
xlab('Index')
plot(p)
# Cook's Distance
cd = cooks.distance(model)
df=tibble::rownames_to_column(as.data.frame(cd),'id')
p=ggplot(data=df,aes(x=as.numeric(id),y=cd)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
geom_text(data=filter(df,cd>15/nrow(train)),aes(label=id),check_overlap=T,size=3,vjust=-.5)+
ylab('Cooks distances') +
geom_hline(yintercept = c(4/nrow(train),0),size=1)+
xlab('Index')
plot(p)
print (paste("Number of data points that have Cook's D > 4/n: ", length(cd[cd > 4/nrow(train)]), sep = ""))
print (paste("Number of data points that have Cook's D > 1: ", length(cd[cd > 1]), sep = ""))
return(cd)
}
# function to set up random seeds
# Based on http://jaehyeon-kim.github.io/2015/05/Setup-Random-Seeds-on-Caret-Package.html
setCaretSeeds <- function(method = "cv", numbers = 1, repeats = 1, tunes = NULL, seed = 1701) {
#B is the number of resamples and integer vector of M (numbers + tune length if any)
B <- if (method == "cv") numbers
else if(method == "repeatedcv") numbers * repeats
else NULL
if(is.null(length)) {
seeds <- NULL
} else {
set.seed(seed = seed)
seeds <- vector(mode = "list", length = B)
seeds <- lapply(seeds, function(x) sample.int(n = 1000000
, size = numbers + ifelse(is.null(tunes), 0, tunes)))
seeds[[length(seeds) + 1]] <- sample.int(n = 1000000, size = 1)
}
# return seeds
seeds
}
train.caret.glmselect = function(formula, data, method
,subopt = NULL, feature.names
, train.control = NULL, tune.grid = NULL, pre.proc = NULL){
if(is.null(train.control)){
train.control <- trainControl(method = "cv"
,number = 10
,seeds = setCaretSeeds(method = "cv"
, numbers = 10
, seed = 1701)
,search = "grid"
,verboseIter = TRUE
,allowParallel = TRUE
)
}
if(is.null(tune.grid)){
if (method == 'leapForward' | method == 'leapBackward' | method == 'leapSeq'){
tune.grid = data.frame(nvmax = 1:length(feature.names))
}
if (method == 'glmnet' && subopt == 'LASSO'){
# Will only show 1 Lambda value during training, but that is OK
# https://stackoverflow.com/questions/47526544/why-need-to-tune-lambda-with-carettrain-method-glmnet-and-cv-glmnet
# Another option for LASSO is this: https://github.com/topepo/caret/blob/master/RegressionTests/Code/lasso.R
lambda = 10^seq(-2,0, length =100)
alpha = c(1)
tune.grid = expand.grid(alpha = alpha,lambda = lambda)
}
if (method == 'lars'){
# https://github.com/topepo/caret/blob/master/RegressionTests/Code/lars.R
fraction = seq(0, 1, length = 100)
tune.grid = expand.grid(fraction = fraction)
pre.proc = c("center", "scale")
}
}
# http://sshaikh.org/2015/05/06/parallelize-machine-learning-in-r-with-multi-core-cpus/
cl <- makeCluster(ceiling(detectCores()*0.85)) # use 75% of cores only, leave rest for other tasks
registerDoParallel(cl)
set.seed(1)
# note that the seed has to actually be set just before this function is called
# settign is above just not ensure reproducibility for some reason
model.caret <- caret::train(formula
, data = data
, method = method
, tuneGrid = tune.grid
, trControl = train.control
, preProc = pre.proc
)
stopCluster(cl)
registerDoSEQ() # register sequential engine in case you are not using this function anymore
if (method == 'leapForward' | method == 'leapBackward' | method == 'leapSeq'){
print("All models results")
print(model.caret$results) # all model results
print("Best Model")
print(model.caret$bestTune) # best model
model = model.caret$finalModel
# Metrics Plot
dataPlot = model.caret$results %>%
gather(key='metric',value='value',-nvmax) %>%
dplyr::filter(metric %in% c('MAE','RMSE','Rsquared'))
metricsPlot = ggplot(data=dataPlot,aes(x=nvmax,y=value) ) +
geom_line(color='lightblue4') +
geom_point(color='blue',alpha=0.7,size=.9) +
facet_wrap(~metric,ncol=2,scales='free')+
theme_light()
plot(metricsPlot)
# Residuals Plot
# leap function does not support studentized residuals
dataPlot=data.frame(pred=predict(model.caret,data),res=resid(model.caret))
residPlot = ggplot(dataPlot,aes(x=pred,y=res)) +
geom_point(color='light blue',alpha=0.7) +
geom_smooth(method="lm")+
theme_light()
plot(residPlot)
residHistogram = ggplot(dataPlot,aes(x=res)) +
geom_histogram(aes(y=..density..),fill='light blue',alpha=1) +
#geom_density(color='lightblue4') +
stat_function(fun = dnorm, n = 100, args = list(mean = mean(dataPlot$res)
, sd = sd(dataPlot$res)),color='lightblue4')
theme_light()
plot(residHistogram)
id = rownames(model.caret$bestTune)
# Provides the coefficients of the best model
# regsubsets doens return a full model (see documentation of regsubset), so we need to recalcualte themodel
# https://stackoverflow.com/questions/13063762/how-to-obtain-a-lm-object-from-regsubsets
print("Coefficients of final model:")
coefs <- coef(model, id=id)
#calculate the model to the the coef intervals
nams <- names(coefs)
nams <- nams[!nams %in% "(Intercept)"]
response <- as.character(formula[[2]])
form <- as.formula(paste(response, paste(nams, collapse = " + "), sep = " ~ "))
mod <- lm(form, data = data)
#coefs
#coef(mod)
print(car::Confint(mod))
return(list(model = model,id = id, residPlot = residPlot, residHistogram=residHistogram
,modelLM=mod))
}
if (method == 'glmnet' && subopt == 'LASSO'){
print(model.caret)
print(plot(model.caret))
print(model.caret$bestTune)
print(model.caret$results)
model=model.caret$finalModel
# Metrics Plot
dataPlot = model.caret$results %>%
gather(key='metric',value='value',-lambda) %>%
dplyr::filter(metric %in% c('MAE','RMSE','Rsquared'))
metricsPlot = ggplot(data=dataPlot,aes(x=lambda,y=value) ) +
geom_line(color='lightblue4') +
geom_point(color='blue',alpha=0.7,size=.9) +
facet_wrap(~metric,ncol=2,scales='free')+
theme_light()
plot(metricsPlot)
# Residuals Plot
dataPlot=data.frame(pred=predict(model.caret,data),res=resid(model.caret))
residPlot = ggplot(dataPlot,aes(x=pred,y=res)) +
geom_point(color='light blue',alpha=0.7) +
geom_smooth(method="lm")+
theme_light()
plot(residPlot)
residHistogram = ggplot(dataPlot,aes(x=res)) +
geom_histogram(aes(y=..density..),fill='light blue',alpha=1) +
#geom_density(color='lightblue4') +
stat_function(fun = dnorm, n = 100, args = list(mean = mean(dataPlot$res)
, sd = sd(dataPlot$res)),color='lightblue4')
theme_light()
plot(residHistogram)
print("Coefficients")
#no interval for glmnet: https://stackoverflow.com/questions/39750965/confidence-intervals-for-ridge-regression
t=coef(model,s=model.caret$bestTune$lambda)
model.coef = t[which(t[,1]!=0),]
print(as.data.frame(model.coef))
id = NULL # not really needed but added for consistency
return(list(model = model.caret,id = id, residPlot = residPlot, metricsPlot=metricsPlot ))
}
if (method == 'lars'){
print(model.caret)
print(plot(model.caret))
print(model.caret$bestTune)
# Metrics Plot
dataPlot = model.caret$results %>%
gather(key='metric',value='value',-fraction) %>%
dplyr::filter(metric %in% c('MAE','RMSE','Rsquared'))
metricsPlot = ggplot(data=dataPlot,aes(x=fraction,y=value) ) +
geom_line(color='lightblue4') +
geom_point(color='blue',alpha=0.7,size=.9) +
facet_wrap(~metric,ncol=2,scales='free')+
theme_light()
plot(metricsPlot)
# Residuals Plot
dataPlot=data.frame(pred=predict(model.caret,data),res=resid(model.caret))
residPlot = ggplot(dataPlot,aes(x=pred,y=res)) +
geom_point(color='light blue',alpha=0.7) +
geom_smooth(method="lm")+
theme_light()
plot(residPlot)
residHistogram = ggplot(dataPlot,aes(x=res)) +
geom_histogram(aes(y=..density..),fill='light blue',alpha=1) +
#geom_density(color='lightblue4') +
stat_function(fun = dnorm, n = 100, args = list(mean = mean(dataPlot$res)
, sd = sd(dataPlot$res)),color='lightblue4')
theme_light()
plot(residHistogram)
print("Coefficients")
t=coef(model.caret$finalModel,s=model.caret$bestTune$fraction,mode='fraction')
model.coef = t[which(t!=0)]
print(model.coef)
id = NULL # not really needed but added for consistency
return(list(model = model.caret,id = id, residPlot = residPlot, residHistogram=residHistogram))
}
}
# https://stackoverflow.com/questions/48265743/linear-model-subset-selection-goodness-of-fit-with-k-fold-cross-validation
# changed slightly since call[[2]] was just returning "formula" without actually returnign the value in formula
predict.regsubsets <- function(object, newdata, id, formula, ...) {
#form <- as.formula(object$call[[2]])
mat <- model.matrix(formula, newdata) # adds intercept and expands any interaction terms
coefi <- coef(object, id = id)
xvars <- names(coefi)
return(mat[,xvars]%*%coefi)
}
test.model = function(model, test, level=0.95
,draw.limits = FALSE, good = 0.1, ok = 0.15
,method = NULL, subopt = NULL
,id = NULL, formula, feature.names, label.names
,transformation = NULL){
## if using caret for glm select equivalent functionality,
## need to pass formula (full is ok as it will select subset of variables from there)
if (is.null(method)){
pred = predict(model, newdata=test, interval="confidence", level = level)
}
if (method == 'leapForward' | method == 'leapBackward' | method == 'leapSeq'){
pred = predict.regsubsets(model, newdata = test, id = id, formula = formula)
}
if (method == 'glmnet' && subopt == 'LASSO'){
xtest = as.matrix(test[,feature.names])
pred=as.data.frame(predict(model, xtest))
}
if (method == 'lars'){
pred=as.data.frame(predict(model, newdata = test))
}
# Summary of predicted values
print ("Summary of predicted values: ")
print(summary(pred[,1]))
test.mse = mean((test[,label.names]-pred[,1])^2)
print (paste(method, subopt, "Test MSE:", test.mse, sep=" "))
if(log.pred == TRUE || norm.pred == TRUE){
# plot transformewd comparison first
df=data.frame(x=test[,label.names],y=pred[,1])
ggplot(df,aes(x=x,y=y)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
geom_abline(slope=1,intercept=0,color='black',size=1) +
#scale_y_continuous(limits=c(min(df),max(df)))+
xlab("Actual (Transformed)")+
ylab("Predicted (Transformed)")
}
if (log.pred == FALSE && norm.pred == FALSE){
x = test[,label.names]
y = pred[,1]
}
if (log.pred == TRUE){
x = 10^test[,label.names]
y = 10^pred[,1]
}
if (norm.pred == TRUE){
x = predict(transformation, test[,label.names], inverse = TRUE)
y = predict(transformation, pred[,1], inverse = TRUE)
}
df=data.frame(x,y)
ggplot(df,aes(x,y)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
geom_abline(slope=c(1+good,1-good,1+ok,1-ok)
,intercept=rep(0,4),color=c('dark green','dark green','dark red','dark red'),size=1,alpha=0.8) +
#scale_y_continuous(limits=c(min(df),max(df)))+
xlab("Actual")+
ylab("Predicted")
}
n <- names(data.train)
formula <- as.formula(paste(paste(n[n %in% label.names], collapse = " + ")
," ~", paste(n[!n %in% label.names], collapse = " + ")))
grand.mean.formula = as.formula(paste(paste(n[n %in% label.names], collapse = " + ")," ~ 1"))
print(formula)
## y3.log ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + x11 +
## x12 + x13 + x14 + x15 + x16 + x17 + x19 + x20 + x21 + x22 +
## x23 + stat1 + stat2 + stat3 + stat4 + stat5 + stat6 + stat7 +
## stat8 + stat9 + stat10 + stat11 + stat12 + stat13 + stat14 +
## stat15 + stat16 + stat17 + stat18 + stat19 + stat20 + stat21 +
## stat22 + stat23 + stat24 + stat25 + stat26 + stat27 + stat28 +
## stat29 + stat30 + stat31 + stat32 + stat33 + stat34 + stat35 +
## stat36 + stat37 + stat38 + stat39 + stat40 + stat41 + stat42 +
## stat43 + stat44 + stat45 + stat46 + stat47 + stat48 + stat49 +
## stat50 + stat51 + stat52 + stat53 + stat54 + stat55 + stat56 +
## stat57 + stat58 + stat59 + stat60 + stat61 + stat62 + stat63 +
## stat64 + stat65 + stat66 + stat67 + stat68 + stat69 + stat70 +
## stat71 + stat72 + stat73 + stat74 + stat75 + stat76 + stat77 +
## stat78 + stat79 + stat80 + stat81 + stat82 + stat83 + stat84 +
## stat85 + stat86 + stat87 + stat88 + stat89 + stat90 + stat91 +
## stat92 + stat93 + stat94 + stat95 + stat96 + stat97 + stat98 +
## stat99 + stat100 + stat101 + stat102 + stat103 + stat104 +
## stat105 + stat106 + stat107 + stat108 + stat109 + stat110 +
## stat111 + stat112 + stat113 + stat114 + stat115 + stat116 +
## stat117 + stat118 + stat119 + stat120 + stat121 + stat122 +
## stat123 + stat124 + stat125 + stat126 + stat127 + stat128 +
## stat129 + stat130 + stat131 + stat132 + stat133 + stat134 +
## stat135 + stat136 + stat137 + stat138 + stat139 + stat140 +
## stat141 + stat142 + stat143 + stat144 + stat145 + stat146 +
## stat147 + stat148 + stat149 + stat150 + stat151 + stat152 +
## stat153 + stat154 + stat155 + stat156 + stat157 + stat158 +
## stat159 + stat160 + stat161 + stat162 + stat163 + stat164 +
## stat165 + stat166 + stat167 + stat168 + stat169 + stat170 +
## stat171 + stat172 + stat173 + stat174 + stat175 + stat176 +
## stat177 + stat178 + stat179 + stat180 + stat181 + stat182 +
## stat183 + stat184 + stat185 + stat186 + stat187 + stat188 +
## stat189 + stat190 + stat191 + stat192 + stat193 + stat194 +
## stat195 + stat196 + stat197 + stat198 + stat199 + stat200 +
## stat201 + stat202 + stat203 + stat204 + stat205 + stat206 +
## stat207 + stat208 + stat209 + stat210 + stat211 + stat212 +
## stat213 + stat214 + stat215 + stat216 + stat217 + x18.sqrt
print(grand.mean.formula)
## y3.log ~ 1
# Update feature.names because we may have transformed some features
feature.names = n[!n %in% label.names]
model.full = lm(formula , data.train)
summary(model.full)
##
## Call:
## lm(formula = formula, data = data.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.08178 -0.02067 -0.00471 0.01609 0.18639
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.970e+00 9.556e-03 206.142 < 2e-16 ***
## x1 -6.863e-05 6.498e-04 -0.106 0.915881
## x2 5.008e-05 4.179e-04 0.120 0.904605
## x3 1.337e-04 1.138e-04 1.175 0.240228
## x4 -5.131e-05 9.020e-06 -5.688 1.35e-08 ***
## x5 2.699e-04 2.947e-04 0.916 0.359764
## x6 -2.488e-04 5.985e-04 -0.416 0.677570
## x7 1.130e-02 6.383e-04 17.709 < 2e-16 ***
## x8 4.326e-04 1.477e-04 2.928 0.003421 **
## x9 3.098e-03 3.315e-04 9.344 < 2e-16 ***
## x10 1.321e-03 3.063e-04 4.313 1.64e-05 ***
## x11 1.603e+05 7.391e+04 2.169 0.030132 *
## x12 -1.902e-04 1.878e-04 -1.013 0.311326
## x13 3.608e-05 7.489e-05 0.482 0.630021
## x14 -1.027e-04 3.226e-04 -0.318 0.750218
## x15 -2.033e-05 3.076e-04 -0.066 0.947299
## x16 9.357e-04 2.143e-04 4.366 1.29e-05 ***
## x17 1.654e-03 3.244e-04 5.100 3.52e-07 ***
## x19 3.010e-04 1.653e-04 1.821 0.068680 .
## x20 1.207e-04 1.147e-03 0.105 0.916227
## x21 1.313e-04 4.213e-05 3.115 0.001847 **
## x22 -4.289e-04 3.438e-04 -1.248 0.212236
## x23 -2.949e-04 3.260e-04 -0.905 0.365689
## stat1 -2.484e-04 2.503e-04 -0.992 0.321105
## stat2 1.218e-05 2.468e-04 0.049 0.960647
## stat3 1.824e-04 2.487e-04 0.733 0.463312
## stat4 -5.521e-04 2.484e-04 -2.222 0.026296 *
## stat5 -2.208e-04 2.482e-04 -0.889 0.373802
## stat6 -1.547e-04 2.478e-04 -0.624 0.532420
## stat7 -1.437e-04 2.487e-04 -0.578 0.563516
## stat8 3.158e-04 2.485e-04 1.271 0.203879
## stat9 -8.143e-05 2.468e-04 -0.330 0.741472
## stat10 -3.091e-04 2.479e-04 -1.247 0.212454
## stat11 -2.275e-04 2.492e-04 -0.913 0.361337
## stat12 -5.211e-05 2.478e-04 -0.210 0.833444
## stat13 -3.516e-04 2.460e-04 -1.429 0.152977
## stat14 -9.129e-04 2.478e-04 -3.684 0.000232 ***
## stat15 -4.564e-04 2.467e-04 -1.850 0.064417 .
## stat16 1.833e-04 2.476e-04 0.740 0.459108
## stat17 -2.116e-05 2.447e-04 -0.086 0.931105
## stat18 -1.787e-04 2.470e-04 -0.724 0.469329
## stat19 -9.858e-05 2.472e-04 -0.399 0.690112
## stat20 -3.307e-04 2.480e-04 -1.334 0.182388
## stat21 -1.325e-04 2.486e-04 -0.533 0.594097
## stat22 -5.268e-04 2.468e-04 -2.134 0.032886 *
## stat23 7.187e-04 2.465e-04 2.916 0.003564 **
## stat24 -4.782e-04 2.483e-04 -1.926 0.054202 .
## stat25 -5.482e-04 2.461e-04 -2.227 0.025973 *
## stat26 -2.560e-04 2.456e-04 -1.043 0.297167
## stat27 7.786e-05 2.487e-04 0.313 0.754268
## stat28 -9.652e-05 2.473e-04 -0.390 0.696361
## stat29 1.491e-04 2.493e-04 0.598 0.549822
## stat30 3.020e-04 2.512e-04 1.202 0.229229
## stat31 -6.386e-05 2.515e-04 -0.254 0.799563
## stat32 1.056e-04 2.508e-04 0.421 0.673699
## stat33 -2.304e-04 2.480e-04 -0.929 0.352959
## stat34 1.075e-04 2.468e-04 0.435 0.663256
## stat35 -5.684e-04 2.470e-04 -2.301 0.021423 *
## stat36 -9.813e-05 2.478e-04 -0.396 0.692087
## stat37 -5.752e-04 2.517e-04 -2.285 0.022333 *
## stat38 5.418e-04 2.494e-04 2.173 0.029836 *
## stat39 -2.344e-04 2.460e-04 -0.953 0.340839
## stat40 4.738e-05 2.482e-04 0.191 0.848628
## stat41 -6.205e-04 2.463e-04 -2.519 0.011804 *
## stat42 -3.248e-04 2.479e-04 -1.310 0.190087
## stat43 -2.760e-04 2.500e-04 -1.104 0.269573
## stat44 1.183e-04 2.483e-04 0.477 0.633699
## stat45 -3.276e-04 2.475e-04 -1.324 0.185697
## stat46 3.546e-04 2.473e-04 1.434 0.151635
## stat47 -2.842e-05 2.486e-04 -0.114 0.908990
## stat48 2.542e-04 2.477e-04 1.026 0.304777
## stat49 2.000e-04 2.463e-04 0.812 0.416818
## stat50 7.916e-05 2.456e-04 0.322 0.747192
## stat51 2.703e-04 2.473e-04 1.093 0.274348
## stat52 -2.712e-04 2.478e-04 -1.095 0.273746
## stat53 -2.500e-04 2.497e-04 -1.001 0.316923
## stat54 -4.110e-04 2.500e-04 -1.644 0.100192
## stat55 1.406e-04 2.447e-04 0.575 0.565631
## stat56 -2.634e-04 2.476e-04 -1.064 0.287411
## stat57 -3.385e-06 2.449e-04 -0.014 0.988972
## stat58 -4.144e-05 2.468e-04 -0.168 0.866656
## stat59 3.593e-04 2.476e-04 1.451 0.146848
## stat60 5.944e-04 2.487e-04 2.390 0.016866 *
## stat61 -1.471e-04 2.486e-04 -0.592 0.554073
## stat62 -8.530e-05 2.474e-04 -0.345 0.730298
## stat63 1.823e-04 2.481e-04 0.735 0.462328
## stat64 5.864e-05 2.469e-04 0.238 0.812246
## stat65 -3.736e-04 2.489e-04 -1.501 0.133326
## stat66 2.772e-04 2.535e-04 1.093 0.274334
## stat67 6.872e-06 2.492e-04 0.028 0.978006
## stat68 1.337e-04 2.466e-04 0.542 0.587730
## stat69 1.408e-04 2.482e-04 0.567 0.570508
## stat70 1.925e-04 2.466e-04 0.780 0.435164
## stat71 -3.814e-05 2.452e-04 -0.156 0.876362
## stat72 3.268e-04 2.492e-04 1.311 0.189769
## stat73 1.849e-04 2.478e-04 0.746 0.455710
## stat74 6.229e-05 2.483e-04 0.251 0.801932
## stat75 -6.380e-05 2.489e-04 -0.256 0.797678
## stat76 3.682e-05 2.470e-04 0.149 0.881517
## stat77 -8.797e-05 2.465e-04 -0.357 0.721246
## stat78 -1.196e-04 2.482e-04 -0.482 0.629851
## stat79 -1.945e-04 2.487e-04 -0.782 0.434157
## stat80 2.584e-04 2.480e-04 1.042 0.297565
## stat81 2.283e-04 2.508e-04 0.911 0.362595
## stat82 3.252e-04 2.469e-04 1.317 0.187740
## stat83 -8.618e-05 2.473e-04 -0.348 0.727517
## stat84 -2.504e-04 2.469e-04 -1.014 0.310449
## stat85 2.483e-04 2.492e-04 0.996 0.319100
## stat86 4.428e-05 2.481e-04 0.178 0.858365
## stat87 4.049e-05 2.488e-04 0.163 0.870741
## stat88 -9.589e-05 2.453e-04 -0.391 0.695839
## stat89 -1.515e-04 2.456e-04 -0.617 0.537468
## stat90 -1.667e-04 2.493e-04 -0.669 0.503690
## stat91 -3.512e-04 2.462e-04 -1.427 0.153703
## stat92 -3.541e-04 2.471e-04 -1.433 0.151945
## stat93 -6.548e-05 2.499e-04 -0.262 0.793338
## stat94 -8.931e-05 2.483e-04 -0.360 0.719055
## stat95 -1.625e-04 2.474e-04 -0.657 0.511194
## stat96 -4.889e-04 2.468e-04 -1.981 0.047607 *
## stat97 1.114e-04 2.460e-04 0.453 0.650746
## stat98 3.297e-03 2.426e-04 13.593 < 2e-16 ***
## stat99 3.826e-04 2.486e-04 1.539 0.123847
## stat100 5.573e-04 2.480e-04 2.247 0.024649 *
## stat101 2.894e-07 2.501e-04 0.001 0.999077
## stat102 1.036e-04 2.499e-04 0.414 0.678677
## stat103 -5.811e-04 2.519e-04 -2.307 0.021074 *
## stat104 -1.892e-04 2.477e-04 -0.764 0.444832
## stat105 1.596e-04 2.455e-04 0.650 0.515621
## stat106 -3.576e-04 2.475e-04 -1.445 0.148491
## stat107 8.019e-05 2.480e-04 0.323 0.746472
## stat108 -1.348e-04 2.476e-04 -0.545 0.586090
## stat109 -6.745e-05 2.478e-04 -0.272 0.785510
## stat110 -3.227e-03 2.464e-04 -13.093 < 2e-16 ***
## stat111 -7.776e-05 2.460e-04 -0.316 0.751965
## stat112 -2.546e-05 2.499e-04 -0.102 0.918851
## stat113 -3.882e-04 2.499e-04 -1.553 0.120424
## stat114 6.827e-05 2.479e-04 0.275 0.783051
## stat115 2.100e-04 2.472e-04 0.850 0.395559
## stat116 2.002e-04 2.506e-04 0.799 0.424324
## stat117 1.081e-04 2.491e-04 0.434 0.664400
## stat118 -5.108e-04 2.460e-04 -2.076 0.037927 *
## stat119 2.218e-04 2.483e-04 0.893 0.371742
## stat120 6.950e-05 2.469e-04 0.281 0.778392
## stat121 -2.689e-04 2.478e-04 -1.085 0.277837
## stat122 -1.433e-04 2.463e-04 -0.582 0.560863
## stat123 -2.120e-05 2.522e-04 -0.084 0.933010
## stat124 -1.940e-04 2.477e-04 -0.783 0.433590
## stat125 3.736e-05 2.468e-04 0.151 0.879677
## stat126 2.449e-04 2.459e-04 0.996 0.319196
## stat127 2.319e-05 2.471e-04 0.094 0.925230
## stat128 -1.690e-04 2.462e-04 -0.687 0.492365
## stat129 1.295e-04 2.462e-04 0.526 0.599026
## stat130 2.281e-04 2.496e-04 0.914 0.360818
## stat131 9.077e-05 2.480e-04 0.366 0.714413
## stat132 1.151e-04 2.464e-04 0.467 0.640561
## stat133 1.998e-04 2.477e-04 0.806 0.420069
## stat134 -2.182e-04 2.464e-04 -0.885 0.375959
## stat135 -2.970e-05 2.471e-04 -0.120 0.904321
## stat136 1.480e-05 2.488e-04 0.059 0.952573
## stat137 1.172e-04 2.454e-04 0.478 0.632959
## stat138 -1.551e-04 2.469e-04 -0.628 0.529876
## stat139 3.655e-06 2.500e-04 0.015 0.988334
## stat140 3.697e-05 2.471e-04 0.150 0.881076
## stat141 2.219e-04 2.465e-04 0.900 0.368063
## stat142 -8.024e-05 2.503e-04 -0.321 0.748552
## stat143 2.102e-04 2.473e-04 0.850 0.395429
## stat144 6.758e-04 2.473e-04 2.732 0.006312 **
## stat145 -8.687e-05 2.506e-04 -0.347 0.728862
## stat146 -3.701e-04 2.498e-04 -1.482 0.138526
## stat147 -3.864e-04 2.495e-04 -1.548 0.121607
## stat148 -4.145e-04 2.443e-04 -1.697 0.089830 .
## stat149 -4.791e-04 2.500e-04 -1.916 0.055395 .
## stat150 8.583e-05 2.491e-04 0.345 0.730440
## stat151 -8.858e-05 2.499e-04 -0.354 0.723043
## stat152 -2.637e-04 2.473e-04 -1.066 0.286304
## stat153 3.258e-05 2.516e-04 0.129 0.896982
## stat154 1.469e-04 2.498e-04 0.588 0.556458
## stat155 -2.144e-04 2.462e-04 -0.871 0.383821
## stat156 5.697e-04 2.514e-04 2.266 0.023465 *
## stat157 -1.609e-04 2.458e-04 -0.654 0.512862
## stat158 -2.509e-05 2.514e-04 -0.100 0.920482
## stat159 2.146e-04 2.470e-04 0.869 0.385085
## stat160 8.115e-06 2.480e-04 0.033 0.973894
## stat161 1.319e-04 2.486e-04 0.531 0.595758
## stat162 1.029e-04 2.458e-04 0.419 0.675345
## stat163 -5.019e-05 2.513e-04 -0.200 0.841666
## stat164 3.362e-04 2.496e-04 1.347 0.178027
## stat165 2.758e-05 2.469e-04 0.112 0.911029
## stat166 -2.798e-04 2.454e-04 -1.140 0.254237
## stat167 -1.416e-04 2.471e-04 -0.573 0.566662
## stat168 -3.821e-04 2.476e-04 -1.543 0.122821
## stat169 -3.081e-05 2.486e-04 -0.124 0.901383
## stat170 -1.655e-04 2.481e-04 -0.667 0.504870
## stat171 6.706e-06 2.498e-04 0.027 0.978585
## stat172 1.666e-04 2.475e-04 0.673 0.500939
## stat173 -2.884e-04 2.492e-04 -1.157 0.247305
## stat174 -5.387e-05 2.488e-04 -0.217 0.828605
## stat175 -2.137e-04 2.482e-04 -0.861 0.389264
## stat176 8.150e-05 2.472e-04 0.330 0.741654
## stat177 -1.097e-04 2.496e-04 -0.439 0.660339
## stat178 1.420e-04 2.508e-04 0.566 0.571409
## stat179 1.283e-04 2.480e-04 0.517 0.604879
## stat180 -1.137e-04 2.460e-04 -0.462 0.643946
## stat181 1.680e-04 2.492e-04 0.674 0.500346
## stat182 7.516e-05 2.487e-04 0.302 0.762486
## stat183 4.747e-06 2.485e-04 0.019 0.984763
## stat184 -5.071e-05 2.477e-04 -0.205 0.837816
## stat185 -1.533e-04 2.437e-04 -0.629 0.529253
## stat186 -1.041e-04 2.498e-04 -0.417 0.676742
## stat187 -3.417e-04 2.476e-04 -1.380 0.167680
## stat188 -2.035e-04 2.480e-04 -0.821 0.411894
## stat189 2.199e-04 2.485e-04 0.885 0.376140
## stat190 8.906e-05 2.473e-04 0.360 0.718794
## stat191 -1.377e-04 2.476e-04 -0.556 0.578200
## stat192 -1.280e-04 2.501e-04 -0.512 0.609013
## stat193 3.807e-05 2.510e-04 0.152 0.879449
## stat194 2.531e-04 2.472e-04 1.024 0.305926
## stat195 3.924e-04 2.485e-04 1.579 0.114453
## stat196 -2.738e-04 2.509e-04 -1.091 0.275144
## stat197 -3.489e-05 2.446e-04 -0.143 0.886591
## stat198 -4.807e-04 2.486e-04 -1.934 0.053183 .
## stat199 -2.719e-05 2.445e-04 -0.111 0.911451
## stat200 -7.682e-05 2.437e-04 -0.315 0.752575
## stat201 -1.626e-04 2.476e-04 -0.657 0.511296
## stat202 -2.217e-04 2.499e-04 -0.887 0.375097
## stat203 -8.868e-05 2.463e-04 -0.360 0.718780
## stat204 -6.357e-04 2.455e-04 -2.589 0.009648 **
## stat205 -4.788e-05 2.456e-04 -0.195 0.845406
## stat206 -7.061e-06 2.496e-04 -0.028 0.977429
## stat207 3.499e-04 2.486e-04 1.407 0.159456
## stat208 2.750e-04 2.489e-04 1.105 0.269234
## stat209 1.437e-04 2.461e-04 0.584 0.559344
## stat210 -8.051e-05 2.498e-04 -0.322 0.747214
## stat211 -2.218e-04 2.491e-04 -0.891 0.373216
## stat212 1.354e-04 2.483e-04 0.545 0.585596
## stat213 -1.129e-04 2.490e-04 -0.453 0.650404
## stat214 -2.589e-04 2.468e-04 -1.049 0.294243
## stat215 -2.433e-04 2.473e-04 -0.984 0.325180
## stat216 -1.774e-05 2.483e-04 -0.071 0.943042
## stat217 -8.501e-05 2.479e-04 -0.343 0.731615
## x18.sqrt 2.653e-02 9.419e-04 28.165 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03137 on 5343 degrees of freedom
## Multiple R-squared: 0.2666, Adjusted R-squared: 0.2336
## F-statistic: 8.092 on 240 and 5343 DF, p-value: < 2.2e-16
cd.full = plot.diagnostics(model=model.full, train=data.train)
## [1] "Number of data points that have Cook's D > 4/n: 283"
## [1] "Number of data points that have Cook's D > 1: 0"
high.cd = names(cd.full[cd.full > 4/nrow(data.train)])
data.train2 = data.train[!(rownames(data.train)) %in% high.cd,]
model.full2 = lm(formula , data.train2)
summary(model.full2)
##
## Call:
## lm(formula = formula, data = data.train2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.059672 -0.017473 -0.002468 0.016181 0.070186
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.954e+00 7.844e-03 249.112 < 2e-16 ***
## x1 -1.006e-04 5.332e-04 -0.189 0.850396
## x2 2.787e-04 3.418e-04 0.816 0.414784
## x3 6.475e-05 9.285e-05 0.697 0.485587
## x4 -5.863e-05 7.393e-06 -7.930 2.68e-15 ***
## x5 3.638e-04 2.407e-04 1.512 0.130721
## x6 -4.620e-04 4.900e-04 -0.943 0.345768
## x7 1.225e-02 5.228e-04 23.429 < 2e-16 ***
## x8 5.193e-04 1.209e-04 4.296 1.77e-05 ***
## x9 3.034e-03 2.707e-04 11.207 < 2e-16 ***
## x10 1.667e-03 2.510e-04 6.641 3.44e-11 ***
## x11 2.274e+05 6.071e+04 3.745 0.000182 ***
## x12 -2.858e-05 1.534e-04 -0.186 0.852152
## x13 1.054e-04 6.150e-05 1.713 0.086739 .
## x14 2.813e-05 2.637e-04 0.107 0.915041
## x15 9.537e-07 2.519e-04 0.004 0.996980
## x16 9.754e-04 1.753e-04 5.566 2.75e-08 ***
## x17 1.773e-03 2.658e-04 6.670 2.82e-11 ***
## x19 2.625e-04 1.354e-04 1.938 0.052682 .
## x20 7.106e-04 9.405e-04 0.756 0.449935
## x21 1.404e-04 3.447e-05 4.073 4.71e-05 ***
## x22 -6.247e-04 2.810e-04 -2.223 0.026258 *
## x23 1.560e-05 2.671e-04 0.058 0.953417
## stat1 -2.928e-04 2.047e-04 -1.430 0.152736
## stat2 -2.099e-05 2.021e-04 -0.104 0.917290
## stat3 2.453e-04 2.034e-04 1.206 0.227908
## stat4 -7.082e-04 2.040e-04 -3.472 0.000520 ***
## stat5 -2.878e-04 2.037e-04 -1.413 0.157727
## stat6 -2.288e-04 2.027e-04 -1.129 0.259040
## stat7 -2.218e-04 2.031e-04 -1.092 0.274801
## stat8 1.441e-04 2.031e-04 0.710 0.477996
## stat9 -2.105e-04 2.022e-04 -1.041 0.297965
## stat10 -3.519e-04 2.025e-04 -1.738 0.082270 .
## stat11 -2.708e-04 2.037e-04 -1.329 0.183788
## stat12 -1.873e-04 2.026e-04 -0.924 0.355354
## stat13 -4.118e-04 2.014e-04 -2.044 0.040957 *
## stat14 -1.067e-03 2.026e-04 -5.267 1.44e-07 ***
## stat15 -7.284e-04 2.020e-04 -3.606 0.000314 ***
## stat16 1.821e-05 2.025e-04 0.090 0.928336
## stat17 -1.715e-04 2.005e-04 -0.856 0.392173
## stat18 -6.926e-05 2.020e-04 -0.343 0.731736
## stat19 -2.102e-05 2.029e-04 -0.104 0.917487
## stat20 8.344e-05 2.028e-04 0.411 0.680725
## stat21 -7.701e-05 2.035e-04 -0.378 0.705146
## stat22 -3.973e-04 2.016e-04 -1.971 0.048771 *
## stat23 5.283e-04 2.022e-04 2.612 0.009020 **
## stat24 -5.404e-04 2.035e-04 -2.655 0.007948 **
## stat25 -3.525e-04 2.014e-04 -1.750 0.080146 .
## stat26 -4.003e-04 2.013e-04 -1.989 0.046747 *
## stat27 -8.281e-05 2.042e-04 -0.406 0.685111
## stat28 -1.719e-04 2.025e-04 -0.849 0.395936
## stat29 1.848e-04 2.041e-04 0.905 0.365284
## stat30 1.995e-04 2.052e-04 0.972 0.330931
## stat31 -2.877e-05 2.061e-04 -0.140 0.888980
## stat32 9.292e-05 2.056e-04 0.452 0.651341
## stat33 -2.685e-04 2.030e-04 -1.322 0.186062
## stat34 2.723e-04 2.018e-04 1.349 0.177305
## stat35 -6.636e-04 2.024e-04 -3.279 0.001049 **
## stat36 -4.160e-05 2.030e-04 -0.205 0.837637
## stat37 -3.116e-04 2.063e-04 -1.511 0.130929
## stat38 6.079e-04 2.039e-04 2.982 0.002880 **
## stat39 -2.945e-04 2.007e-04 -1.467 0.142330
## stat40 8.267e-05 2.035e-04 0.406 0.684545
## stat41 -6.399e-04 2.012e-04 -3.181 0.001477 **
## stat42 -1.812e-04 2.029e-04 -0.893 0.371769
## stat43 -1.650e-04 2.042e-04 -0.808 0.419022
## stat44 1.170e-04 2.033e-04 0.576 0.564962
## stat45 -2.082e-04 2.026e-04 -1.028 0.304145
## stat46 3.088e-04 2.027e-04 1.524 0.127661
## stat47 2.265e-04 2.030e-04 1.116 0.264541
## stat48 2.709e-04 2.023e-04 1.339 0.180592
## stat49 -4.536e-05 2.022e-04 -0.224 0.822481
## stat50 1.033e-04 2.008e-04 0.515 0.606793
## stat51 1.737e-05 2.026e-04 0.086 0.931685
## stat52 -6.611e-05 2.027e-04 -0.326 0.744379
## stat53 -1.627e-04 2.044e-04 -0.796 0.426073
## stat54 -3.784e-04 2.051e-04 -1.845 0.065100 .
## stat55 -2.782e-05 2.002e-04 -0.139 0.889491
## stat56 2.477e-05 2.025e-04 0.122 0.902630
## stat57 -1.329e-04 2.009e-04 -0.662 0.508283
## stat58 1.851e-05 2.013e-04 0.092 0.926738
## stat59 3.648e-04 2.025e-04 1.801 0.071687 .
## stat60 5.623e-04 2.032e-04 2.767 0.005675 **
## stat61 -2.213e-04 2.033e-04 -1.089 0.276268
## stat62 -1.958e-04 2.023e-04 -0.968 0.332973
## stat63 1.454e-04 2.037e-04 0.714 0.475190
## stat64 1.307e-04 2.018e-04 0.647 0.517357
## stat65 -2.407e-04 2.036e-04 -1.182 0.237162
## stat66 2.188e-04 2.070e-04 1.057 0.290736
## stat67 -1.933e-05 2.036e-04 -0.095 0.924378
## stat68 -5.693e-05 2.017e-04 -0.282 0.777806
## stat69 1.349e-04 2.032e-04 0.664 0.506619
## stat70 1.750e-04 2.019e-04 0.867 0.386055
## stat71 6.304e-05 2.012e-04 0.313 0.754034
## stat72 1.778e-04 2.041e-04 0.871 0.383742
## stat73 2.600e-04 2.030e-04 1.281 0.200268
## stat74 2.486e-04 2.030e-04 1.225 0.220716
## stat75 1.303e-04 2.037e-04 0.640 0.522230
## stat76 -4.703e-06 2.020e-04 -0.023 0.981432
## stat77 1.447e-04 2.017e-04 0.717 0.473367
## stat78 -3.502e-04 2.028e-04 -1.727 0.084185 .
## stat79 1.699e-04 2.030e-04 0.837 0.402707
## stat80 2.814e-04 2.028e-04 1.388 0.165342
## stat81 8.358e-05 2.055e-04 0.407 0.684175
## stat82 1.103e-04 2.021e-04 0.546 0.585214
## stat83 -1.369e-04 2.026e-04 -0.676 0.499038
## stat84 -3.122e-04 2.017e-04 -1.548 0.121672
## stat85 -1.715e-04 2.041e-04 -0.840 0.400723
## stat86 2.374e-05 2.028e-04 0.117 0.906815
## stat87 2.507e-05 2.035e-04 0.123 0.901973
## stat88 1.306e-04 2.008e-04 0.651 0.515372
## stat89 1.152e-04 2.013e-04 0.572 0.567113
## stat90 -2.045e-04 2.041e-04 -1.002 0.316299
## stat91 -3.246e-04 2.009e-04 -1.615 0.106277
## stat92 -4.085e-04 2.021e-04 -2.021 0.043346 *
## stat93 7.728e-05 2.055e-04 0.376 0.706891
## stat94 -2.198e-05 2.028e-04 -0.108 0.913711
## stat95 1.737e-04 2.031e-04 0.855 0.392589
## stat96 -5.336e-04 2.021e-04 -2.641 0.008300 **
## stat97 2.497e-04 2.009e-04 1.243 0.214083
## stat98 3.355e-03 1.982e-04 16.929 < 2e-16 ***
## stat99 3.620e-04 2.034e-04 1.780 0.075083 .
## stat100 5.890e-04 2.027e-04 2.906 0.003674 **
## stat101 9.050e-05 2.046e-04 0.442 0.658287
## stat102 1.746e-04 2.045e-04 0.854 0.393229
## stat103 -6.227e-04 2.061e-04 -3.021 0.002529 **
## stat104 -1.356e-04 2.032e-04 -0.667 0.504605
## stat105 2.101e-04 2.007e-04 1.046 0.295413
## stat106 -3.913e-04 2.023e-04 -1.934 0.053149 .
## stat107 3.594e-05 2.033e-04 0.177 0.859640
## stat108 -5.122e-05 2.026e-04 -0.253 0.800410
## stat109 -1.632e-04 2.031e-04 -0.803 0.421796
## stat110 -3.159e-03 2.013e-04 -15.689 < 2e-16 ***
## stat111 -3.348e-05 2.010e-04 -0.167 0.867692
## stat112 -2.269e-05 2.046e-04 -0.111 0.911705
## stat113 -2.960e-04 2.044e-04 -1.448 0.147620
## stat114 6.672e-05 2.034e-04 0.328 0.742962
## stat115 3.671e-04 2.025e-04 1.813 0.069944 .
## stat116 2.890e-04 2.049e-04 1.410 0.158471
## stat117 9.480e-05 2.035e-04 0.466 0.641280
## stat118 -2.474e-04 2.015e-04 -1.228 0.219682
## stat119 3.059e-04 2.028e-04 1.508 0.131528
## stat120 -6.368e-05 2.019e-04 -0.315 0.752507
## stat121 -3.261e-04 2.027e-04 -1.609 0.107675
## stat122 -1.608e-04 2.019e-04 -0.796 0.425861
## stat123 2.330e-04 2.060e-04 1.131 0.258192
## stat124 -1.939e-04 2.025e-04 -0.957 0.338448
## stat125 -9.369e-05 2.024e-04 -0.463 0.643373
## stat126 1.675e-04 2.013e-04 0.832 0.405190
## stat127 -6.926e-05 2.017e-04 -0.343 0.731342
## stat128 -3.811e-04 2.009e-04 -1.897 0.057830 .
## stat129 4.311e-05 2.013e-04 0.214 0.830418
## stat130 2.485e-04 2.041e-04 1.218 0.223269
## stat131 1.917e-05 2.028e-04 0.095 0.924694
## stat132 3.908e-05 2.016e-04 0.194 0.846334
## stat133 3.193e-04 2.030e-04 1.573 0.115805
## stat134 -1.567e-04 2.014e-04 -0.778 0.436538
## stat135 -1.540e-04 2.023e-04 -0.761 0.446515
## stat136 -5.277e-05 2.035e-04 -0.259 0.795427
## stat137 9.876e-05 2.007e-04 0.492 0.622760
## stat138 -1.760e-04 2.024e-04 -0.870 0.384555
## stat139 -7.530e-05 2.045e-04 -0.368 0.712721
## stat140 9.920e-05 2.015e-04 0.492 0.622478
## stat141 2.497e-04 2.017e-04 1.238 0.215866
## stat142 -8.143e-05 2.046e-04 -0.398 0.690714
## stat143 5.200e-05 2.023e-04 0.257 0.797158
## stat144 7.088e-04 2.023e-04 3.504 0.000462 ***
## stat145 -2.182e-04 2.054e-04 -1.062 0.288062
## stat146 -6.001e-04 2.043e-04 -2.937 0.003330 **
## stat147 -3.444e-04 2.045e-04 -1.684 0.092190 .
## stat148 -3.123e-04 2.003e-04 -1.559 0.119059
## stat149 -3.351e-04 2.045e-04 -1.638 0.101394
## stat150 -1.043e-04 2.042e-04 -0.511 0.609465
## stat151 2.195e-04 2.053e-04 1.069 0.285008
## stat152 -2.542e-04 2.023e-04 -1.257 0.208852
## stat153 2.024e-04 2.055e-04 0.985 0.324770
## stat154 2.432e-04 2.046e-04 1.189 0.234686
## stat155 -1.390e-04 2.016e-04 -0.690 0.490454
## stat156 5.234e-04 2.053e-04 2.550 0.010810 *
## stat157 -1.696e-04 2.006e-04 -0.845 0.397966
## stat158 2.330e-04 2.055e-04 1.134 0.256993
## stat159 3.911e-04 2.017e-04 1.939 0.052558 .
## stat160 -2.707e-05 2.037e-04 -0.133 0.894290
## stat161 5.193e-05 2.035e-04 0.255 0.798547
## stat162 1.120e-04 2.007e-04 0.558 0.576784
## stat163 1.314e-04 2.063e-04 0.637 0.524066
## stat164 2.301e-04 2.046e-04 1.125 0.260648
## stat165 1.607e-04 2.025e-04 0.793 0.427602
## stat166 -2.457e-04 2.005e-04 -1.226 0.220441
## stat167 -2.124e-04 2.020e-04 -1.052 0.293055
## stat168 -2.128e-04 2.024e-04 -1.052 0.293015
## stat169 -2.002e-04 2.041e-04 -0.981 0.326531
## stat170 1.649e-05 2.030e-04 0.081 0.935260
## stat171 -1.599e-04 2.045e-04 -0.782 0.434133
## stat172 4.611e-04 2.020e-04 2.283 0.022451 *
## stat173 -1.003e-04 2.037e-04 -0.492 0.622492
## stat174 1.386e-04 2.037e-04 0.680 0.496394
## stat175 -8.449e-05 2.029e-04 -0.416 0.677102
## stat176 -1.987e-04 2.022e-04 -0.983 0.325867
## stat177 -3.254e-04 2.041e-04 -1.594 0.110895
## stat178 1.071e-04 2.049e-04 0.523 0.601182
## stat179 6.874e-05 2.030e-04 0.339 0.734939
## stat180 -5.548e-05 2.018e-04 -0.275 0.783403
## stat181 1.769e-04 2.040e-04 0.867 0.385816
## stat182 1.996e-04 2.038e-04 0.979 0.327485
## stat183 2.331e-05 2.037e-04 0.114 0.908904
## stat184 1.267e-04 2.025e-04 0.626 0.531589
## stat185 -7.414e-05 1.995e-04 -0.372 0.710118
## stat186 2.143e-04 2.040e-04 1.051 0.293506
## stat187 -1.355e-04 2.025e-04 -0.669 0.503313
## stat188 -4.129e-05 2.030e-04 -0.203 0.838822
## stat189 -9.430e-05 2.037e-04 -0.463 0.643459
## stat190 -7.275e-05 2.027e-04 -0.359 0.719646
## stat191 -1.645e-04 2.029e-04 -0.811 0.417479
## stat192 -1.536e-05 2.048e-04 -0.075 0.940204
## stat193 1.027e-04 2.056e-04 0.500 0.617238
## stat194 1.954e-04 2.027e-04 0.964 0.335126
## stat195 2.507e-05 2.035e-04 0.123 0.901973
## stat196 -2.533e-04 2.053e-04 -1.234 0.217238
## stat197 -6.852e-05 2.006e-04 -0.342 0.732648
## stat198 -4.724e-04 2.032e-04 -2.325 0.020087 *
## stat199 -2.222e-05 1.999e-04 -0.111 0.911528
## stat200 -2.620e-05 2.000e-04 -0.131 0.895812
## stat201 -7.635e-05 2.028e-04 -0.376 0.706604
## stat202 -6.241e-05 2.045e-04 -0.305 0.760246
## stat203 -2.131e-06 2.016e-04 -0.011 0.991566
## stat204 -4.278e-04 2.012e-04 -2.126 0.033537 *
## stat205 2.614e-04 2.005e-04 1.304 0.192308
## stat206 2.265e-05 2.043e-04 0.111 0.911720
## stat207 3.200e-04 2.037e-04 1.571 0.116291
## stat208 2.732e-04 2.037e-04 1.341 0.179968
## stat209 4.938e-05 2.009e-04 0.246 0.805818
## stat210 -3.287e-04 2.042e-04 -1.609 0.107633
## stat211 -1.374e-04 2.037e-04 -0.674 0.500032
## stat212 1.592e-04 2.032e-04 0.784 0.433367
## stat213 -6.417e-05 2.033e-04 -0.316 0.752321
## stat214 -5.880e-05 2.022e-04 -0.291 0.771161
## stat215 -3.556e-05 2.025e-04 -0.176 0.860585
## stat216 -4.683e-05 2.030e-04 -0.231 0.817546
## stat217 -6.784e-05 2.026e-04 -0.335 0.737703
## x18.sqrt 2.573e-02 7.695e-04 33.442 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.02498 on 5060 degrees of freedom
## Multiple R-squared: 0.3716, Adjusted R-squared: 0.3418
## F-statistic: 12.47 on 240 and 5060 DF, p-value: < 2.2e-16
cd.full2 = plot.diagnostics(model.full2, data.train2)
## [1] "Number of data points that have Cook's D > 4/n: 268"
## [1] "Number of data points that have Cook's D > 1: 0"
# much more normal residuals than before.
# Checking to see if distributions are different and if so whcih variables
# High Leverage Plot
plotData = data.train %>%
rownames_to_column() %>%
mutate(type=ifelse(rowname %in% high.cd,'High','Normal')) %>%
dplyr::select(type,target=one_of(label.names))
ggplot(data=plotData, aes(x=type,y=target)) +
geom_boxplot(fill='light blue',outlier.shape=NA) +
scale_y_continuous(name="Target Variable Values",label=scales::comma_format(accuracy=.1)) +
theme_light() +
ggtitle('Distribution of High Leverage Points and Normal Points')
# 2 sample t-tests
plotData = data.train %>%
rownames_to_column() %>%
mutate(type=ifelse(rowname %in% high.cd,'High','Normal')) %>%
dplyr::select(type,one_of(feature.names))
comp.test = lapply(dplyr::select(plotData, one_of(feature.names))
, function(x) t.test(x ~ plotData$type, var.equal = TRUE))
sig.comp = list.filter(comp.test, p.value < 0.05)
sapply(sig.comp, function(x) x[['p.value']])
## x4 x13 stat47 stat74 stat79 stat85 stat95 stat98 stat110 stat118
## 0.016745266 0.048060296 0.010332348 0.022937363 0.023191401 0.014578179 0.012976838 0.004766528 0.004564928 0.049750199
## stat128 stat146 stat151 stat172 stat174 x18.sqrt
## 0.020931056 0.002432513 0.002668840 0.015474014 0.016114109 0.005719575
mm = melt(plotData, id=c('type')) %>% filter(variable %in% names(sig.comp))
ggplot(mm,aes(x=type, y=value)) +
geom_boxplot()+
facet_wrap(~variable, ncol=5, scales = 'free_y') +
scale_y_continuous(name="values",label=scales::comma_format(accuracy=.1)) +
ggtitle('Distribution of High Leverage Points and Normal Points')
# Distribution (box) Plots
mm = melt(plotData, id=c('type'))
ggplot(mm,aes(x=type, y=value)) +
geom_boxplot()+
facet_wrap(~variable, ncol=8, scales = 'free_y') +
scale_y_continuous(name="values",label=scales::comma_format(accuracy=.1)) +
ggtitle('Distribution of High Leverage Points and Normal Points')
model.null = lm(grand.mean.formula, data.train)
summary(model.null)
##
## Call:
## lm(formula = grand.mean.formula, data = data.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.114447 -0.023670 -0.003088 0.020699 0.190865
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.0963232 0.0004796 4371 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03584 on 5583 degrees of freedom
Basic: http://www.stat.columbia.edu/~martin/W2024/R10.pdf Cross Validation + Other Metrics: http://www.sthda.com/english/articles/37-model-selection-essentials-in-r/154-stepwise-regression-essentials-in-r/
if (algo.forward.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
, data = data.train
, method = "leapForward"
, feature.names = feature.names)
model.forward = returned$model
id = returned$id
}
## Aggregating results
## Selecting tuning parameters
## Fitting nvmax = 9 on full training set
## [1] "All models results"
## nvmax RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 1 0.03376443 0.1132051 0.02637850 0.001210125 0.02571127 0.0007953495
## 2 2 0.03297241 0.1543836 0.02566825 0.001331813 0.02849647 0.0008195492
## 3 3 0.03250196 0.1779147 0.02515184 0.001317023 0.02808594 0.0007621952
## 4 4 0.03196246 0.2052676 0.02446499 0.001452681 0.03363383 0.0008687720
## 5 5 0.03171086 0.2179498 0.02429750 0.001512147 0.03600988 0.0008518664
## 6 6 0.03165522 0.2206821 0.02425311 0.001516391 0.03578302 0.0008635422
## 7 7 0.03161930 0.2224386 0.02422076 0.001591134 0.03757869 0.0009392440
## 8 8 0.03155244 0.2257309 0.02419734 0.001617014 0.03868599 0.0009624076
## 9 9 0.03146134 0.2301155 0.02411499 0.001613656 0.03869431 0.0009595924
## 10 10 0.03148846 0.2287059 0.02413610 0.001591183 0.03762129 0.0009509402
## 11 11 0.03149049 0.2285003 0.02414479 0.001570434 0.03691604 0.0009354630
## 12 12 0.03150288 0.2280520 0.02416044 0.001590991 0.03717482 0.0009408043
## 13 13 0.03147622 0.2293254 0.02413800 0.001586666 0.03717877 0.0009728358
## 14 14 0.03148550 0.2289291 0.02413604 0.001600811 0.03767695 0.0009991203
## 15 15 0.03151049 0.2277667 0.02415137 0.001606362 0.03779119 0.0009983448
## 16 16 0.03151635 0.2273578 0.02416525 0.001572932 0.03632568 0.0009714183
## 17 17 0.03150438 0.2281246 0.02415982 0.001625619 0.03860212 0.0010191859
## 18 18 0.03148935 0.2287951 0.02414977 0.001611874 0.03811350 0.0009983158
## 19 19 0.03151416 0.2275893 0.02417693 0.001615300 0.03794160 0.0009956441
## 20 20 0.03152056 0.2272807 0.02417600 0.001596570 0.03716561 0.0009803289
## 21 21 0.03154669 0.2261143 0.02419830 0.001617907 0.03751442 0.0009939951
## 22 22 0.03154258 0.2263547 0.02419706 0.001629603 0.03753844 0.0009951548
## 23 23 0.03153604 0.2267287 0.02419708 0.001655219 0.03857136 0.0010094637
## 24 24 0.03155255 0.2260822 0.02419265 0.001684882 0.03957765 0.0010268588
## 25 25 0.03155408 0.2260284 0.02418587 0.001689191 0.03990833 0.0010270298
## 26 26 0.03154873 0.2262955 0.02416219 0.001685026 0.03986879 0.0010210127
## 27 27 0.03155328 0.2260303 0.02416425 0.001663973 0.03967169 0.0010144567
## 28 28 0.03155382 0.2260225 0.02416367 0.001663828 0.03962532 0.0010069188
## 29 29 0.03156583 0.2254547 0.02418043 0.001651293 0.03897893 0.0009943649
## 30 30 0.03155684 0.2258888 0.02415646 0.001638154 0.03841906 0.0009837442
## 31 31 0.03153999 0.2266618 0.02414505 0.001632233 0.03819485 0.0009886043
## 32 32 0.03151698 0.2277475 0.02412685 0.001637437 0.03866256 0.0009879513
## 33 33 0.03151831 0.2276883 0.02413576 0.001645905 0.03911899 0.0009916034
## 34 34 0.03151883 0.2276606 0.02413974 0.001631469 0.03880302 0.0009744988
## 35 35 0.03154507 0.2264281 0.02416116 0.001629429 0.03864976 0.0009707139
## 36 36 0.03156000 0.2257663 0.02417609 0.001637191 0.03888266 0.0009651906
## 37 37 0.03157255 0.2252214 0.02417586 0.001629348 0.03887564 0.0009433069
## 38 38 0.03157709 0.2250000 0.02417403 0.001619733 0.03834612 0.0009490266
## 39 39 0.03158311 0.2246788 0.02418235 0.001608177 0.03811691 0.0009327292
## 40 40 0.03157660 0.2249812 0.02417328 0.001601715 0.03802827 0.0009333391
## 41 41 0.03157994 0.2248479 0.02417578 0.001598479 0.03767096 0.0009240815
## 42 42 0.03159280 0.2243115 0.02419645 0.001610375 0.03793595 0.0009412851
## 43 43 0.03161078 0.2235172 0.02420986 0.001619250 0.03824488 0.0009352708
## 44 44 0.03161571 0.2233960 0.02421582 0.001629535 0.03815850 0.0009466490
## 45 45 0.03163338 0.2225880 0.02423854 0.001624007 0.03781633 0.0009572754
## 46 46 0.03165357 0.2217409 0.02424698 0.001638198 0.03833703 0.0009517115
## 47 47 0.03165045 0.2218831 0.02425060 0.001641539 0.03855126 0.0009613354
## 48 48 0.03165229 0.2218124 0.02424900 0.001635124 0.03801085 0.0009475429
## 49 49 0.03165748 0.2215394 0.02426206 0.001617272 0.03745263 0.0009329003
## 50 50 0.03165576 0.2216631 0.02426824 0.001626231 0.03760716 0.0009422135
## 51 51 0.03165318 0.2218348 0.02425618 0.001646914 0.03847422 0.0009634940
## 52 52 0.03164534 0.2222132 0.02425384 0.001650135 0.03854186 0.0009693838
## 53 53 0.03164915 0.2220794 0.02425284 0.001655188 0.03864325 0.0009803038
## 54 54 0.03166404 0.2214448 0.02426685 0.001661344 0.03888532 0.0009801524
## 55 55 0.03167813 0.2208456 0.02428079 0.001654840 0.03868200 0.0009720576
## 56 56 0.03169254 0.2202632 0.02428812 0.001671027 0.03923630 0.0009800438
## 57 57 0.03169290 0.2202503 0.02428713 0.001660515 0.03880597 0.0009792344
## 58 58 0.03170811 0.2196494 0.02430801 0.001675331 0.03929542 0.0009813584
## 59 59 0.03170832 0.2196100 0.02430829 0.001679190 0.03949799 0.0009876783
## 60 60 0.03171442 0.2193722 0.02431397 0.001681803 0.03940761 0.0009880787
## 61 61 0.03171827 0.2192246 0.02431394 0.001682356 0.03954285 0.0009945707
## 62 62 0.03172933 0.2186956 0.02431744 0.001675110 0.03925966 0.0009916646
## 63 63 0.03173473 0.2184783 0.02431872 0.001676780 0.03925339 0.0009919249
## 64 64 0.03174445 0.2180452 0.02432738 0.001664626 0.03860308 0.0009848951
## 65 65 0.03174443 0.2180567 0.02433362 0.001667985 0.03876814 0.0009845751
## 66 66 0.03175913 0.2173833 0.02433572 0.001659284 0.03839698 0.0009783930
## 67 67 0.03178079 0.2164414 0.02435910 0.001664050 0.03827764 0.0009732358
## 68 68 0.03178756 0.2161682 0.02436393 0.001664038 0.03809367 0.0009690576
## 69 69 0.03178825 0.2161694 0.02436803 0.001659617 0.03798711 0.0009643715
## 70 70 0.03178399 0.2163411 0.02436652 0.001655424 0.03792377 0.0009597160
## 71 71 0.03179906 0.2156736 0.02437714 0.001647574 0.03757939 0.0009528316
## 72 72 0.03179416 0.2158477 0.02437399 0.001631353 0.03675672 0.0009342997
## 73 73 0.03179572 0.2157435 0.02437089 0.001612803 0.03599641 0.0009218926
## 74 74 0.03180787 0.2152322 0.02438424 0.001614303 0.03595790 0.0009241667
## 75 75 0.03181700 0.2148192 0.02439246 0.001610985 0.03605262 0.0009237233
## 76 76 0.03182615 0.2144628 0.02440048 0.001624772 0.03671604 0.0009362699
## 77 77 0.03183813 0.2139326 0.02440424 0.001625314 0.03655623 0.0009278254
## 78 78 0.03183733 0.2140381 0.02440092 0.001636449 0.03700436 0.0009362784
## 79 79 0.03184456 0.2137585 0.02439755 0.001630896 0.03670791 0.0009275353
## 80 80 0.03184634 0.2136726 0.02439934 0.001627336 0.03657316 0.0009292705
## 81 81 0.03184712 0.2136560 0.02440049 0.001632079 0.03670798 0.0009339735
## 82 82 0.03185246 0.2133743 0.02439837 0.001624579 0.03631407 0.0009321499
## 83 83 0.03185596 0.2132599 0.02439630 0.001615867 0.03578217 0.0009218415
## 84 84 0.03186888 0.2127285 0.02441174 0.001622706 0.03584910 0.0009243956
## 85 85 0.03187198 0.2125986 0.02441358 0.001622276 0.03585038 0.0009269831
## 86 86 0.03187488 0.2125116 0.02441085 0.001626148 0.03589743 0.0009260710
## 87 87 0.03188425 0.2120934 0.02442174 0.001623465 0.03567756 0.0009244922
## 88 88 0.03189377 0.2116576 0.02443020 0.001625477 0.03584241 0.0009306201
## 89 89 0.03189489 0.2115921 0.02442992 0.001611914 0.03543400 0.0009244797
## 90 90 0.03189803 0.2114880 0.02443294 0.001621994 0.03592825 0.0009350216
## 91 91 0.03189387 0.2116790 0.02443728 0.001624224 0.03617286 0.0009445513
## 92 92 0.03190258 0.2113163 0.02444987 0.001630018 0.03618382 0.0009481915
## 93 93 0.03191214 0.2109291 0.02446380 0.001625956 0.03589556 0.0009439625
## 94 94 0.03191953 0.2106278 0.02447116 0.001634376 0.03621845 0.0009504174
## 95 95 0.03192174 0.2105287 0.02447374 0.001639284 0.03646714 0.0009494909
## 96 96 0.03192383 0.2104574 0.02447592 0.001647418 0.03679894 0.0009502987
## 97 97 0.03192138 0.2105360 0.02447681 0.001645036 0.03661491 0.0009444669
## 98 98 0.03192558 0.2103441 0.02448593 0.001638947 0.03641185 0.0009402478
## 99 99 0.03193996 0.2097225 0.02450039 0.001634728 0.03603204 0.0009324637
## 100 100 0.03194713 0.2093916 0.02450688 0.001631410 0.03583493 0.0009282906
## 101 101 0.03195059 0.2092510 0.02450933 0.001633273 0.03589106 0.0009284388
## 102 102 0.03195079 0.2092721 0.02450903 0.001636954 0.03604166 0.0009276216
## 103 103 0.03195039 0.2092890 0.02451361 0.001634318 0.03600958 0.0009288547
## 104 104 0.03194778 0.2094480 0.02450635 0.001647475 0.03641458 0.0009352793
## 105 105 0.03195300 0.2092568 0.02450945 0.001653611 0.03653122 0.0009386915
## 106 106 0.03194676 0.2095200 0.02450036 0.001652690 0.03645639 0.0009413139
## 107 107 0.03194424 0.2096773 0.02450002 0.001657674 0.03680850 0.0009457516
## 108 108 0.03194396 0.2096988 0.02449708 0.001665709 0.03720448 0.0009561827
## 109 109 0.03194474 0.2097188 0.02450526 0.001674121 0.03755448 0.0009649439
## 110 110 0.03195409 0.2093471 0.02451377 0.001679231 0.03763577 0.0009648311
## 111 111 0.03195493 0.2093532 0.02450762 0.001680674 0.03768724 0.0009664962
## 112 112 0.03195505 0.2093891 0.02450460 0.001681926 0.03753329 0.0009662913
## 113 113 0.03195344 0.2095011 0.02451027 0.001682498 0.03754671 0.0009621606
## 114 114 0.03194959 0.2096658 0.02450635 0.001679427 0.03746315 0.0009609270
## 115 115 0.03195215 0.2095677 0.02450614 0.001681046 0.03754224 0.0009651858
## 116 116 0.03194839 0.2097654 0.02450252 0.001681647 0.03757296 0.0009651146
## 117 117 0.03195556 0.2094604 0.02451090 0.001681443 0.03752031 0.0009654871
## 118 118 0.03195898 0.2093186 0.02451724 0.001680721 0.03740338 0.0009643888
## 119 119 0.03196935 0.2088877 0.02452516 0.001679762 0.03727511 0.0009707635
## 120 120 0.03196945 0.2088651 0.02452932 0.001671420 0.03695710 0.0009620223
## 121 121 0.03197467 0.2086596 0.02453194 0.001676487 0.03718816 0.0009648268
## 122 122 0.03197439 0.2086852 0.02453554 0.001676644 0.03725109 0.0009658998
## 123 123 0.03198316 0.2083381 0.02453924 0.001679531 0.03743020 0.0009680243
## 124 124 0.03198606 0.2082206 0.02453967 0.001673898 0.03715531 0.0009599227
## 125 125 0.03198593 0.2082440 0.02453984 0.001676011 0.03722132 0.0009602820
## 126 126 0.03199250 0.2079521 0.02454583 0.001682366 0.03741507 0.0009644955
## 127 127 0.03199796 0.2077411 0.02454516 0.001691226 0.03772996 0.0009768143
## 128 128 0.03200385 0.2074923 0.02454675 0.001693681 0.03777845 0.0009797929
## 129 129 0.03200606 0.2074080 0.02454354 0.001693154 0.03785897 0.0009819511
## 130 130 0.03200100 0.2076367 0.02454008 0.001689598 0.03782988 0.0009808613
## 131 131 0.03200213 0.2076187 0.02454153 0.001696574 0.03808547 0.0009836103
## 132 132 0.03200088 0.2076828 0.02454062 0.001702009 0.03817866 0.0009870940
## 133 133 0.03200424 0.2075501 0.02454504 0.001701815 0.03820049 0.0009836945
## 134 134 0.03200675 0.2074742 0.02454620 0.001710244 0.03849383 0.0009903456
## 135 135 0.03201056 0.2073325 0.02455297 0.001717647 0.03875545 0.0009971011
## 136 136 0.03201873 0.2070125 0.02455705 0.001722382 0.03886395 0.0010013594
## 137 137 0.03201720 0.2070643 0.02455675 0.001719466 0.03890377 0.0009997024
## 138 138 0.03201959 0.2069799 0.02455816 0.001718972 0.03892620 0.0009972627
## 139 139 0.03202704 0.2066557 0.02456806 0.001719693 0.03896455 0.0009997890
## 140 140 0.03203111 0.2064998 0.02457047 0.001726596 0.03921937 0.0010020771
## 141 141 0.03203204 0.2064275 0.02456939 0.001723251 0.03921163 0.0010054752
## 142 142 0.03203737 0.2062058 0.02457312 0.001721927 0.03921771 0.0010009187
## 143 143 0.03203468 0.2063634 0.02457031 0.001730254 0.03955454 0.0010098625
## 144 144 0.03203194 0.2065047 0.02456799 0.001734497 0.03960300 0.0010138648
## 145 145 0.03202888 0.2066253 0.02456749 0.001732453 0.03949143 0.0010101781
## 146 146 0.03202900 0.2065828 0.02456817 0.001726149 0.03926183 0.0010086948
## 147 147 0.03203265 0.2064451 0.02456831 0.001728947 0.03934584 0.0010082405
## 148 148 0.03203265 0.2064716 0.02456818 0.001729942 0.03937349 0.0010105181
## 149 149 0.03203925 0.2062020 0.02457187 0.001729300 0.03941662 0.0010134382
## 150 150 0.03204270 0.2060345 0.02457140 0.001728513 0.03939170 0.0010124932
## 151 151 0.03204191 0.2060832 0.02457259 0.001732850 0.03951611 0.0010177971
## 152 152 0.03204591 0.2059142 0.02457287 0.001732439 0.03946691 0.0010154070
## 153 153 0.03204730 0.2058458 0.02457219 0.001732411 0.03941944 0.0010128432
## 154 154 0.03204789 0.2058192 0.02457299 0.001728224 0.03930249 0.0010124778
## 155 155 0.03204728 0.2058491 0.02457448 0.001729026 0.03937989 0.0010112018
## 156 156 0.03204863 0.2057925 0.02457229 0.001730239 0.03938558 0.0010079784
## 157 157 0.03205002 0.2057508 0.02457339 0.001733028 0.03944596 0.0010087673
## 158 158 0.03204928 0.2058014 0.02457474 0.001735593 0.03957032 0.0010092366
## 159 159 0.03205041 0.2057696 0.02457329 0.001737223 0.03966633 0.0010096001
## 160 160 0.03205335 0.2056615 0.02457434 0.001736527 0.03962676 0.0010107099
## 161 161 0.03205277 0.2056699 0.02457582 0.001733803 0.03952035 0.0010093485
## 162 162 0.03205657 0.2055293 0.02457856 0.001737473 0.03959675 0.0010106169
## 163 163 0.03205895 0.2054412 0.02458144 0.001742425 0.03980948 0.0010120838
## 164 164 0.03206061 0.2053590 0.02457867 0.001739526 0.03967356 0.0010072814
## 165 165 0.03205824 0.2054717 0.02457618 0.001740622 0.03973945 0.0010081460
## 166 166 0.03205788 0.2054671 0.02457549 0.001737660 0.03965766 0.0010084729
## 167 167 0.03205856 0.2054331 0.02457806 0.001734901 0.03963067 0.0010096999
## 168 168 0.03205826 0.2054423 0.02458130 0.001736207 0.03967999 0.0010107704
## 169 169 0.03205653 0.2055342 0.02458053 0.001738721 0.03978588 0.0010118609
## 170 170 0.03205692 0.2055109 0.02457902 0.001739632 0.03986380 0.0010096672
## 171 171 0.03205964 0.2054054 0.02457857 0.001741526 0.03999012 0.0010113802
## 172 172 0.03205775 0.2054849 0.02457659 0.001744494 0.04013054 0.0010120259
## 173 173 0.03206104 0.2053320 0.02457814 0.001742426 0.04004003 0.0010091491
## 174 174 0.03206154 0.2053388 0.02457995 0.001745361 0.04016413 0.0010114263
## 175 175 0.03206326 0.2052625 0.02458365 0.001748928 0.04030923 0.0010152442
## 176 176 0.03206449 0.2052126 0.02458324 0.001749031 0.04023667 0.0010146625
## 177 177 0.03206468 0.2051944 0.02458241 0.001745893 0.04014386 0.0010125679
## 178 178 0.03206690 0.2050950 0.02458418 0.001746059 0.04020591 0.0010140861
## 179 179 0.03206963 0.2049935 0.02458641 0.001744099 0.04012297 0.0010125982
## 180 180 0.03206824 0.2050605 0.02458589 0.001747495 0.04029491 0.0010137075
## 181 181 0.03206783 0.2050861 0.02458614 0.001748000 0.04032684 0.0010137868
## 182 182 0.03206601 0.2051526 0.02458461 0.001745317 0.04022556 0.0010134454
## 183 183 0.03206719 0.2051005 0.02458521 0.001740300 0.04005921 0.0010120811
## 184 184 0.03206570 0.2051739 0.02458287 0.001740030 0.04000019 0.0010109548
## 185 185 0.03206394 0.2052533 0.02458097 0.001739748 0.03994777 0.0010113347
## 186 186 0.03206590 0.2051779 0.02458136 0.001742400 0.04003026 0.0010123898
## 187 187 0.03206373 0.2052643 0.02457841 0.001739239 0.03995552 0.0010106592
## 188 188 0.03206450 0.2052473 0.02457848 0.001741928 0.04004459 0.0010128976
## 189 189 0.03206461 0.2052330 0.02457829 0.001742197 0.04008339 0.0010143514
## 190 190 0.03206515 0.2052026 0.02457903 0.001743699 0.04011418 0.0010144082
## 191 191 0.03206830 0.2050664 0.02458149 0.001743854 0.04008097 0.0010129111
## 192 192 0.03207039 0.2049842 0.02458347 0.001745013 0.04009942 0.0010152572
## 193 193 0.03206917 0.2050420 0.02458126 0.001743709 0.04006825 0.0010159651
## 194 194 0.03206973 0.2050280 0.02458116 0.001742525 0.04005330 0.0010148770
## 195 195 0.03207123 0.2049603 0.02458130 0.001741862 0.04000480 0.0010143535
## 196 196 0.03207069 0.2049848 0.02458195 0.001742802 0.04005671 0.0010153305
## 197 197 0.03206869 0.2050826 0.02457892 0.001745123 0.04013938 0.0010161935
## 198 198 0.03206907 0.2050597 0.02457929 0.001745878 0.04017312 0.0010187940
## 199 199 0.03206995 0.2050216 0.02458109 0.001746296 0.04016722 0.0010193117
## 200 200 0.03206896 0.2050647 0.02457954 0.001748017 0.04025962 0.0010197098
## 201 201 0.03206883 0.2050716 0.02457940 0.001748384 0.04024545 0.0010207262
## 202 202 0.03206772 0.2051314 0.02457711 0.001749645 0.04029812 0.0010228163
## 203 203 0.03206745 0.2051314 0.02457619 0.001744907 0.04014658 0.0010186347
## 204 204 0.03206770 0.2051181 0.02457536 0.001745263 0.04015378 0.0010182995
## 205 205 0.03206632 0.2051692 0.02457445 0.001742740 0.04006480 0.0010177920
## 206 206 0.03206751 0.2051218 0.02457500 0.001743598 0.04009224 0.0010198099
## 207 207 0.03206897 0.2050495 0.02457577 0.001741183 0.04002018 0.0010176988
## 208 208 0.03206968 0.2050207 0.02457615 0.001739870 0.03996805 0.0010155763
## 209 209 0.03206953 0.2050276 0.02457688 0.001738998 0.03991646 0.0010149879
## 210 210 0.03207019 0.2050072 0.02457752 0.001739041 0.03990977 0.0010156110
## 211 211 0.03207051 0.2049941 0.02457788 0.001736662 0.03982307 0.0010140456
## 212 212 0.03207207 0.2049278 0.02457917 0.001735638 0.03979933 0.0010141485
## 213 213 0.03207192 0.2049312 0.02457959 0.001734728 0.03977390 0.0010133716
## 214 214 0.03207326 0.2048654 0.02458110 0.001732864 0.03970858 0.0010122239
## 215 215 0.03207362 0.2048447 0.02458269 0.001731383 0.03964952 0.0010114171
## 216 216 0.03207405 0.2048244 0.02458258 0.001730747 0.03962130 0.0010105264
## 217 217 0.03207360 0.2048493 0.02458291 0.001730862 0.03962953 0.0010117337
## 218 218 0.03207367 0.2048519 0.02458347 0.001732159 0.03967375 0.0010137218
## 219 219 0.03207287 0.2048856 0.02458252 0.001731865 0.03966546 0.0010142560
## 220 220 0.03207280 0.2048914 0.02458221 0.001731415 0.03964697 0.0010147703
## 221 221 0.03207320 0.2048780 0.02458173 0.001731722 0.03966011 0.0010147500
## 222 222 0.03207325 0.2048653 0.02458192 0.001730936 0.03963943 0.0010142181
## 223 223 0.03207242 0.2049032 0.02458086 0.001732350 0.03968642 0.0010157095
## 224 224 0.03207233 0.2049031 0.02458054 0.001731883 0.03966506 0.0010149805
## 225 225 0.03207208 0.2049147 0.02458105 0.001731677 0.03965140 0.0010147254
## 226 226 0.03207187 0.2049254 0.02458114 0.001731322 0.03964074 0.0010143681
## 227 227 0.03207190 0.2049216 0.02458136 0.001730803 0.03962087 0.0010141621
## 228 228 0.03207191 0.2049236 0.02458172 0.001730910 0.03963172 0.0010141598
## 229 229 0.03207167 0.2049328 0.02458197 0.001730707 0.03962512 0.0010136789
## 230 230 0.03207144 0.2049413 0.02458189 0.001730667 0.03962483 0.0010132987
## 231 231 0.03207139 0.2049460 0.02458187 0.001730581 0.03962191 0.0010130583
## 232 232 0.03207141 0.2049454 0.02458210 0.001730423 0.03961255 0.0010130997
## 233 233 0.03207113 0.2049573 0.02458187 0.001730504 0.03961599 0.0010128952
## 234 234 0.03207138 0.2049481 0.02458204 0.001730713 0.03961909 0.0010130771
## 235 235 0.03207144 0.2049436 0.02458214 0.001730248 0.03960528 0.0010129099
## 236 236 0.03207155 0.2049378 0.02458225 0.001729964 0.03959589 0.0010128528
## 237 237 0.03207166 0.2049333 0.02458232 0.001730128 0.03959893 0.0010132226
## 238 238 0.03207158 0.2049367 0.02458219 0.001730269 0.03960374 0.0010132711
## 239 239 0.03207162 0.2049353 0.02458225 0.001730332 0.03960637 0.0010133297
## 240 240 0.03207168 0.2049328 0.02458231 0.001730399 0.03960843 0.0010134866
## [1] "Best Model"
## nvmax
## 9 9
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## [1] "Coefficients of final model:"
## Estimate 2.5 % 97.5 %
## (Intercept) 1.997430e+00 1.990899e+00 2.003962e+00
## x4 -5.115588e-05 -6.853808e-05 -3.377368e-05
## x7 1.102188e-02 9.794023e-03 1.224974e-02
## x9 3.070804e-03 2.432449e-03 3.709159e-03
## x10 1.278875e-03 6.873502e-04 1.870401e-03
## x16 9.700205e-04 5.568889e-04 1.383152e-03
## x17 1.600779e-03 9.763881e-04 2.225170e-03
## stat98 3.343631e-03 2.875903e-03 3.811359e-03
## stat110 -3.137873e-03 -3.613099e-03 -2.662647e-03
## x18.sqrt 2.631786e-02 2.450088e-02 2.813484e-02
if (algo.forward.caret == TRUE){
test.model(model=model.forward, test=data.test
,method = 'leapForward',subopt = NULL
,formula = formula, feature.names = feature.names, label.names = label.names
,id = id
,draw.limits = TRUE, transformation = t)
}
## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.044 2.084 2.097 2.096 2.108 2.145
## [1] "leapForward Test MSE: 0.00104102201936567"
if (algo.backward.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
,data = data.train
,method = "leapBackward"
,feature.names = feature.names)
model.backward = returned$model
id = returned$id
}
## Aggregating results
## Selecting tuning parameters
## Fitting nvmax = 9 on full training set
## [1] "All models results"
## nvmax RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 1 0.03376443 0.1132051 0.02637850 0.001210125 0.02571127 0.0007953495
## 2 2 0.03297241 0.1543836 0.02566825 0.001331813 0.02849647 0.0008195492
## 3 3 0.03250196 0.1779147 0.02515184 0.001317023 0.02808594 0.0007621952
## 4 4 0.03196246 0.2052676 0.02446499 0.001452681 0.03363383 0.0008687720
## 5 5 0.03171086 0.2179498 0.02429750 0.001512147 0.03600988 0.0008518664
## 6 6 0.03165522 0.2206821 0.02425311 0.001516391 0.03578302 0.0008635422
## 7 7 0.03161930 0.2224386 0.02422076 0.001591134 0.03757869 0.0009392440
## 8 8 0.03155244 0.2257309 0.02419734 0.001617014 0.03868599 0.0009624076
## 9 9 0.03146134 0.2301155 0.02411499 0.001613656 0.03869431 0.0009595924
## 10 10 0.03148846 0.2287059 0.02413610 0.001591183 0.03762129 0.0009509402
## 11 11 0.03149049 0.2285003 0.02414479 0.001570434 0.03691604 0.0009354630
## 12 12 0.03150288 0.2280520 0.02416044 0.001590991 0.03717482 0.0009408043
## 13 13 0.03147622 0.2293254 0.02413800 0.001586666 0.03717877 0.0009728358
## 14 14 0.03148550 0.2289291 0.02413604 0.001600811 0.03767695 0.0009991203
## 15 15 0.03151049 0.2277667 0.02415137 0.001606362 0.03779119 0.0009983448
## 16 16 0.03151635 0.2273578 0.02416525 0.001572932 0.03632568 0.0009714183
## 17 17 0.03151854 0.2274304 0.02417083 0.001620733 0.03851447 0.0010107519
## 18 18 0.03151706 0.2274435 0.02417252 0.001612832 0.03798687 0.0010024230
## 19 19 0.03150643 0.2279334 0.02417277 0.001614284 0.03758714 0.0009928002
## 20 20 0.03151455 0.2275297 0.02416644 0.001601300 0.03679747 0.0009782668
## 21 21 0.03152350 0.2272073 0.02417310 0.001616084 0.03729289 0.0009942840
## 22 22 0.03153133 0.2268917 0.02418051 0.001637620 0.03791465 0.0010081285
## 23 23 0.03153472 0.2267931 0.02419805 0.001654486 0.03865559 0.0010016789
## 24 24 0.03154107 0.2265226 0.02418155 0.001654418 0.03873667 0.0009895126
## 25 25 0.03155055 0.2260937 0.02418320 0.001655011 0.03888933 0.0009942238
## 26 26 0.03156946 0.2253051 0.02418445 0.001671881 0.03942483 0.0010103395
## 27 27 0.03156320 0.2255405 0.02417591 0.001656519 0.03929361 0.0010097896
## 28 28 0.03155968 0.2256921 0.02416543 0.001641156 0.03889225 0.0009961736
## 29 29 0.03156008 0.2257004 0.02417187 0.001632050 0.03851225 0.0009880978
## 30 30 0.03155303 0.2260316 0.02415863 0.001638438 0.03866867 0.0010092221
## 31 31 0.03154030 0.2265958 0.02415053 0.001633024 0.03834113 0.0010009403
## 32 32 0.03151614 0.2277098 0.02413535 0.001635320 0.03874525 0.0010068959
## 33 33 0.03151612 0.2277270 0.02413915 0.001633799 0.03880826 0.0009846613
## 34 34 0.03152601 0.2273383 0.02414968 0.001637943 0.03907524 0.0009900342
## 35 35 0.03155330 0.2260819 0.02416139 0.001631636 0.03882983 0.0009646840
## 36 36 0.03156681 0.2254905 0.02417513 0.001634204 0.03899492 0.0009505969
## 37 37 0.03156984 0.2253640 0.02417301 0.001627327 0.03899171 0.0009414108
## 38 38 0.03158292 0.2247439 0.02417679 0.001626142 0.03852619 0.0009428337
## 39 39 0.03159319 0.2242198 0.02418826 0.001606407 0.03783241 0.0009290149
## 40 40 0.03159669 0.2240627 0.02418838 0.001605620 0.03793335 0.0009231437
## 41 41 0.03159141 0.2243412 0.02418673 0.001597770 0.03758194 0.0009218706
## 42 42 0.03160271 0.2238269 0.02420513 0.001602599 0.03744318 0.0009346345
## 43 43 0.03162291 0.2229319 0.02422565 0.001613625 0.03779303 0.0009251648
## 44 44 0.03161870 0.2232648 0.02422728 0.001634643 0.03844407 0.0009409630
## 45 45 0.03162575 0.2229534 0.02423617 0.001629968 0.03831795 0.0009594620
## 46 46 0.03164307 0.2222409 0.02424256 0.001646312 0.03900960 0.0009557584
## 47 47 0.03164253 0.2222972 0.02424679 0.001650969 0.03910748 0.0009549745
## 48 48 0.03164846 0.2220330 0.02424821 0.001642169 0.03838372 0.0009513925
## 49 49 0.03164170 0.2223116 0.02424750 0.001632779 0.03832009 0.0009456064
## 50 50 0.03164476 0.2222214 0.02425721 0.001642346 0.03859620 0.0009515632
## 51 51 0.03165193 0.2219214 0.02425602 0.001652095 0.03874678 0.0009640624
## 52 52 0.03166112 0.2215574 0.02425967 0.001665668 0.03901083 0.0009741897
## 53 53 0.03165650 0.2218185 0.02425549 0.001668125 0.03904165 0.0009865959
## 54 54 0.03166885 0.2213211 0.02426931 0.001679554 0.03956173 0.0009859223
## 55 55 0.03168163 0.2207730 0.02428046 0.001674059 0.03929660 0.0009798176
## 56 56 0.03168683 0.2205238 0.02428724 0.001666329 0.03898309 0.0009758769
## 57 57 0.03169172 0.2202992 0.02429299 0.001660758 0.03877914 0.0009719258
## 58 58 0.03170084 0.2199577 0.02430556 0.001680169 0.03936789 0.0009869420
## 59 59 0.03170868 0.2195765 0.02430840 0.001686251 0.03970138 0.0009934343
## 60 60 0.03171373 0.2193797 0.02430721 0.001685401 0.03967520 0.0009924490
## 61 61 0.03172095 0.2190824 0.02430536 0.001683846 0.03983444 0.0009859919
## 62 62 0.03173676 0.2183728 0.02431540 0.001676745 0.03924955 0.0009840450
## 63 63 0.03173566 0.2184635 0.02431800 0.001675287 0.03931261 0.0009796601
## 64 64 0.03174800 0.2179168 0.02433325 0.001663164 0.03862511 0.0009698114
## 65 65 0.03175247 0.2177127 0.02433372 0.001664481 0.03870935 0.0009669790
## 66 66 0.03177087 0.2168375 0.02434812 0.001652297 0.03786732 0.0009683765
## 67 67 0.03177685 0.2166231 0.02435198 0.001667331 0.03838883 0.0009768701
## 68 68 0.03177916 0.2165151 0.02434921 0.001653032 0.03788144 0.0009635538
## 69 69 0.03178149 0.2164660 0.02435498 0.001647806 0.03762553 0.0009509664
## 70 70 0.03178028 0.2165100 0.02436229 0.001640233 0.03734418 0.0009446900
## 71 71 0.03179564 0.2158159 0.02437843 0.001632269 0.03710029 0.0009381754
## 72 72 0.03180255 0.2155075 0.02437518 0.001632268 0.03687301 0.0009382289
## 73 73 0.03180341 0.2154291 0.02437042 0.001613656 0.03618860 0.0009237270
## 74 74 0.03180664 0.2153014 0.02438649 0.001615000 0.03627773 0.0009253223
## 75 75 0.03181452 0.2149576 0.02439193 0.001614592 0.03640882 0.0009285769
## 76 76 0.03183510 0.2140674 0.02441256 0.001625175 0.03662858 0.0009327369
## 77 77 0.03183378 0.2141269 0.02440372 0.001624565 0.03641434 0.0009283979
## 78 78 0.03184326 0.2137857 0.02440586 0.001636562 0.03695941 0.0009348021
## 79 79 0.03184414 0.2137899 0.02439668 0.001632421 0.03674510 0.0009286141
## 80 80 0.03184240 0.2138410 0.02439629 0.001623171 0.03645926 0.0009226085
## 81 81 0.03184355 0.2138035 0.02439771 0.001630765 0.03664124 0.0009296515
## 82 82 0.03185316 0.2133683 0.02440806 0.001627985 0.03638365 0.0009316153
## 83 83 0.03185331 0.2134055 0.02440493 0.001626828 0.03621102 0.0009318230
## 84 84 0.03185812 0.2131926 0.02441273 0.001621493 0.03605908 0.0009229377
## 85 85 0.03185973 0.2131309 0.02441101 0.001615861 0.03568937 0.0009215410
## 86 86 0.03187074 0.2126741 0.02442318 0.001622649 0.03604431 0.0009273429
## 87 87 0.03187398 0.2125347 0.02442644 0.001628812 0.03630578 0.0009341526
## 88 88 0.03187304 0.2125894 0.02442682 0.001627924 0.03615784 0.0009347815
## 89 89 0.03186499 0.2129482 0.02442956 0.001620726 0.03615265 0.0009321775
## 90 90 0.03187006 0.2127345 0.02443499 0.001619794 0.03599117 0.0009368625
## 91 91 0.03187912 0.2123591 0.02444726 0.001627911 0.03637699 0.0009475462
## 92 92 0.03188901 0.2119675 0.02445430 0.001633350 0.03661004 0.0009471446
## 93 93 0.03190221 0.2114126 0.02446904 0.001639925 0.03685801 0.0009531317
## 94 94 0.03191062 0.2110209 0.02447440 0.001637373 0.03671421 0.0009500144
## 95 95 0.03191444 0.2108484 0.02447644 0.001643076 0.03686508 0.0009497913
## 96 96 0.03193166 0.2101177 0.02449032 0.001649354 0.03697641 0.0009477463
## 97 97 0.03193476 0.2100126 0.02449239 0.001646448 0.03665186 0.0009469300
## 98 98 0.03193593 0.2099594 0.02449311 0.001642868 0.03637415 0.0009446989
## 99 99 0.03194040 0.2098085 0.02450478 0.001648869 0.03662896 0.0009504618
## 100 100 0.03194567 0.2095663 0.02451329 0.001653175 0.03667706 0.0009473889
## 101 101 0.03194332 0.2096481 0.02450551 0.001654923 0.03669238 0.0009494527
## 102 102 0.03195094 0.2093602 0.02450876 0.001658724 0.03680229 0.0009459566
## 103 103 0.03195150 0.2093222 0.02451137 0.001656284 0.03683249 0.0009426637
## 104 104 0.03194431 0.2096316 0.02450884 0.001659702 0.03693890 0.0009467433
## 105 105 0.03193967 0.2098606 0.02450051 0.001665449 0.03727246 0.0009495248
## 106 106 0.03194176 0.2098140 0.02450074 0.001675530 0.03763435 0.0009585169
## 107 107 0.03194515 0.2097282 0.02450124 0.001681835 0.03782683 0.0009629241
## 108 108 0.03195052 0.2095448 0.02450451 0.001690632 0.03801944 0.0009753126
## 109 109 0.03195337 0.2094251 0.02450302 0.001685034 0.03780720 0.0009707768
## 110 110 0.03196040 0.2090924 0.02450908 0.001677944 0.03751180 0.0009695303
## 111 111 0.03196052 0.2091093 0.02450686 0.001679228 0.03740028 0.0009686649
## 112 112 0.03196368 0.2090227 0.02451285 0.001685651 0.03759708 0.0009712771
## 113 113 0.03195830 0.2092894 0.02451325 0.001683738 0.03769225 0.0009717533
## 114 114 0.03196448 0.2090170 0.02451843 0.001682308 0.03764379 0.0009729096
## 115 115 0.03196050 0.2092388 0.02451512 0.001686512 0.03767290 0.0009736178
## 116 116 0.03196352 0.2091128 0.02451980 0.001686154 0.03767998 0.0009740847
## 117 117 0.03196711 0.2089605 0.02452610 0.001684090 0.03757049 0.0009708766
## 118 118 0.03196965 0.2088583 0.02452959 0.001679011 0.03733576 0.0009670367
## 119 119 0.03196947 0.2088370 0.02452608 0.001673010 0.03707106 0.0009615711
## 120 120 0.03197392 0.2086510 0.02452973 0.001668032 0.03684659 0.0009593368
## 121 121 0.03197411 0.2086483 0.02452961 0.001669335 0.03690322 0.0009593472
## 122 122 0.03197685 0.2085641 0.02453581 0.001674711 0.03712505 0.0009689956
## 123 123 0.03198324 0.2083040 0.02453964 0.001678748 0.03737788 0.0009746737
## 124 124 0.03199337 0.2078714 0.02454828 0.001679221 0.03730500 0.0009737390
## 125 125 0.03199364 0.2078678 0.02454760 0.001682188 0.03744509 0.0009750597
## 126 126 0.03199575 0.2077564 0.02455053 0.001682908 0.03740870 0.0009767111
## 127 127 0.03199795 0.2076857 0.02454423 0.001681225 0.03736124 0.0009751879
## 128 128 0.03200211 0.2075362 0.02454392 0.001690064 0.03767706 0.0009786170
## 129 129 0.03200455 0.2074668 0.02454282 0.001694358 0.03793396 0.0009826791
## 130 130 0.03200390 0.2075405 0.02454280 0.001698883 0.03815146 0.0009839730
## 131 131 0.03200625 0.2074741 0.02454332 0.001708004 0.03846112 0.0009900765
## 132 132 0.03200289 0.2076352 0.02454190 0.001716637 0.03870799 0.0009984791
## 133 133 0.03200790 0.2074340 0.02454655 0.001715338 0.03865955 0.0009919718
## 134 134 0.03201373 0.2072098 0.02455047 0.001718614 0.03884604 0.0009939049
## 135 135 0.03201610 0.2071012 0.02455662 0.001718211 0.03883545 0.0009972249
## 136 136 0.03202107 0.2069231 0.02456087 0.001723037 0.03895849 0.0010002304
## 137 137 0.03202205 0.2068609 0.02456044 0.001717656 0.03881638 0.0009982568
## 138 138 0.03202430 0.2067610 0.02456189 0.001715968 0.03875214 0.0009935655
## 139 139 0.03203175 0.2064532 0.02456804 0.001720138 0.03889162 0.0009923886
## 140 140 0.03203003 0.2065156 0.02456911 0.001720819 0.03906064 0.0009986241
## 141 141 0.03203095 0.2064841 0.02456690 0.001721875 0.03917149 0.0009975847
## 142 142 0.03203701 0.2062293 0.02457037 0.001721090 0.03918567 0.0010013638
## 143 143 0.03203248 0.2064534 0.02456847 0.001727144 0.03939548 0.0010094938
## 144 144 0.03203004 0.2065512 0.02456533 0.001725724 0.03935372 0.0010066377
## 145 145 0.03202781 0.2066199 0.02456512 0.001723152 0.03920696 0.0010072855
## 146 146 0.03202867 0.2065976 0.02456735 0.001727172 0.03933727 0.0010101899
## 147 147 0.03203087 0.2065116 0.02456887 0.001728624 0.03941244 0.0010122912
## 148 148 0.03203364 0.2064273 0.02457026 0.001732490 0.03958166 0.0010147771
## 149 149 0.03204024 0.2061508 0.02457446 0.001731066 0.03947658 0.0010145296
## 150 150 0.03204280 0.2060230 0.02457340 0.001730403 0.03942516 0.0010151918
## 151 151 0.03204141 0.2060872 0.02457115 0.001734455 0.03957117 0.0010218562
## 152 152 0.03204300 0.2060226 0.02456864 0.001733689 0.03946074 0.0010174451
## 153 153 0.03204505 0.2059347 0.02457140 0.001732184 0.03939813 0.0010130176
## 154 154 0.03204641 0.2058849 0.02457278 0.001729495 0.03940792 0.0010148582
## 155 155 0.03204793 0.2058252 0.02457399 0.001728896 0.03940343 0.0010122740
## 156 156 0.03205108 0.2056920 0.02457397 0.001729682 0.03940055 0.0010073055
## 157 157 0.03204971 0.2057734 0.02457339 0.001734533 0.03956170 0.0010095181
## 158 158 0.03204901 0.2058135 0.02457365 0.001736523 0.03964971 0.0010096661
## 159 159 0.03204906 0.2058248 0.02457177 0.001737911 0.03966948 0.0010102455
## 160 160 0.03204874 0.2058629 0.02457097 0.001737810 0.03965245 0.0010125979
## 161 161 0.03205296 0.2056876 0.02457500 0.001738080 0.03962469 0.0010101045
## 162 162 0.03205761 0.2055122 0.02457869 0.001742117 0.03975448 0.0010109296
## 163 163 0.03206178 0.2053210 0.02458069 0.001742289 0.03971724 0.0010066157
## 164 164 0.03205688 0.2055257 0.02457507 0.001742000 0.03979812 0.0010101092
## 165 165 0.03205838 0.2054506 0.02457697 0.001740489 0.03972717 0.0010073238
## 166 166 0.03205829 0.2054295 0.02457574 0.001738206 0.03969447 0.0010085867
## 167 167 0.03205831 0.2054351 0.02457826 0.001735121 0.03961186 0.0010087757
## 168 168 0.03205708 0.2055010 0.02457956 0.001737201 0.03969842 0.0010108297
## 169 169 0.03205765 0.2054833 0.02458242 0.001737848 0.03975777 0.0010095326
## 170 170 0.03205692 0.2055109 0.02457902 0.001739632 0.03986380 0.0010096672
## 171 171 0.03205840 0.2054563 0.02457740 0.001741787 0.03998514 0.0010116398
## 172 172 0.03206066 0.2053646 0.02457968 0.001746255 0.04023872 0.0010136217
## 173 173 0.03206337 0.2052442 0.02458318 0.001747884 0.04023816 0.0010178862
## 174 174 0.03206302 0.2052716 0.02458261 0.001750363 0.04035796 0.0010179336
## 175 175 0.03206267 0.2052794 0.02458317 0.001748168 0.04029320 0.0010135216
## 176 176 0.03206449 0.2052126 0.02458324 0.001749031 0.04023667 0.0010146625
## 177 177 0.03206468 0.2051944 0.02458241 0.001745893 0.04014386 0.0010125679
## 178 178 0.03206690 0.2050950 0.02458418 0.001746059 0.04020591 0.0010140861
## 179 179 0.03206963 0.2049935 0.02458641 0.001744099 0.04012297 0.0010125982
## 180 180 0.03206868 0.2050381 0.02458600 0.001747179 0.04027861 0.0010136997
## 181 181 0.03206663 0.2051288 0.02458658 0.001745268 0.04023468 0.0010138553
## 182 182 0.03206500 0.2051892 0.02458547 0.001743100 0.04014883 0.0010145327
## 183 183 0.03206835 0.2050578 0.02458614 0.001743329 0.04016153 0.0010144200
## 184 184 0.03206652 0.2051432 0.02458384 0.001742172 0.04007395 0.0010134162
## 185 185 0.03206504 0.2052120 0.02458092 0.001742836 0.04005249 0.0010144394
## 186 186 0.03206671 0.2051392 0.02458023 0.001741803 0.04000189 0.0010129632
## 187 187 0.03206473 0.2052182 0.02457762 0.001738734 0.03994668 0.0010113227
## 188 188 0.03206629 0.2051647 0.02457988 0.001741694 0.04002117 0.0010136551
## 189 189 0.03206730 0.2051053 0.02458020 0.001741748 0.04005787 0.0010148205
## 190 190 0.03206552 0.2051807 0.02457924 0.001743614 0.04011565 0.0010143605
## 191 191 0.03206896 0.2050331 0.02458283 0.001744766 0.04012691 0.0010136410
## 192 192 0.03207025 0.2049907 0.02458290 0.001744863 0.04009111 0.0010145145
## 193 193 0.03206830 0.2050794 0.02458018 0.001743904 0.04007501 0.0010155272
## 194 194 0.03206718 0.2051318 0.02457819 0.001743454 0.04007019 0.0010162075
## 195 195 0.03206803 0.2050948 0.02457807 0.001743314 0.04006339 0.0010159525
## 196 196 0.03206899 0.2050562 0.02457941 0.001743544 0.04008443 0.0010166987
## 197 197 0.03206869 0.2050826 0.02457892 0.001745123 0.04013938 0.0010161935
## 198 198 0.03206855 0.2050853 0.02457905 0.001745915 0.04016540 0.0010189015
## 199 199 0.03206919 0.2050596 0.02458065 0.001746714 0.04018099 0.0010193463
## 200 200 0.03206777 0.2051261 0.02457848 0.001748371 0.04026181 0.0010201048
## 201 201 0.03206832 0.2050969 0.02457912 0.001748421 0.04023792 0.0010208528
## 202 202 0.03206772 0.2051314 0.02457711 0.001749645 0.04029812 0.0010228163
## 203 203 0.03206745 0.2051314 0.02457619 0.001744907 0.04014658 0.0010186347
## 204 204 0.03206800 0.2051065 0.02457627 0.001745241 0.04015729 0.0010178985
## 205 205 0.03206728 0.2051326 0.02457580 0.001742674 0.04007599 0.0010171964
## 206 206 0.03206777 0.2051166 0.02457590 0.001743580 0.04009384 0.0010194146
## 207 207 0.03206837 0.2050758 0.02457590 0.001741224 0.04001211 0.0010176408
## 208 208 0.03206968 0.2050207 0.02457615 0.001739870 0.03996805 0.0010155763
## 209 209 0.03206953 0.2050276 0.02457688 0.001738998 0.03991646 0.0010149879
## 210 210 0.03207019 0.2050072 0.02457752 0.001739041 0.03990977 0.0010156110
## 211 211 0.03207051 0.2049941 0.02457788 0.001736662 0.03982307 0.0010140456
## 212 212 0.03207207 0.2049278 0.02457917 0.001735638 0.03979933 0.0010141485
## 213 213 0.03207192 0.2049312 0.02457959 0.001734728 0.03977390 0.0010133716
## 214 214 0.03207326 0.2048654 0.02458110 0.001732864 0.03970858 0.0010122239
## 215 215 0.03207362 0.2048447 0.02458269 0.001731383 0.03964952 0.0010114171
## 216 216 0.03207405 0.2048244 0.02458258 0.001730747 0.03962130 0.0010105264
## 217 217 0.03207360 0.2048493 0.02458291 0.001730862 0.03962953 0.0010117337
## 218 218 0.03207367 0.2048519 0.02458347 0.001732159 0.03967375 0.0010137218
## 219 219 0.03207287 0.2048856 0.02458252 0.001731865 0.03966546 0.0010142560
## 220 220 0.03207260 0.2048978 0.02458218 0.001731602 0.03965058 0.0010148007
## 221 221 0.03207300 0.2048841 0.02458170 0.001731904 0.03966357 0.0010147819
## 222 222 0.03207325 0.2048653 0.02458192 0.001730936 0.03963943 0.0010142181
## 223 223 0.03207242 0.2049032 0.02458086 0.001732350 0.03968642 0.0010157095
## 224 224 0.03207233 0.2049031 0.02458054 0.001731883 0.03966506 0.0010149805
## 225 225 0.03207208 0.2049147 0.02458105 0.001731677 0.03965140 0.0010147254
## 226 226 0.03207187 0.2049254 0.02458114 0.001731322 0.03964074 0.0010143681
## 227 227 0.03207190 0.2049216 0.02458136 0.001730803 0.03962087 0.0010141621
## 228 228 0.03207191 0.2049236 0.02458172 0.001730910 0.03963172 0.0010141598
## 229 229 0.03207167 0.2049328 0.02458197 0.001730707 0.03962512 0.0010136789
## 230 230 0.03207144 0.2049413 0.02458189 0.001730667 0.03962483 0.0010132987
## 231 231 0.03207139 0.2049460 0.02458187 0.001730581 0.03962191 0.0010130583
## 232 232 0.03207141 0.2049454 0.02458210 0.001730423 0.03961255 0.0010130997
## 233 233 0.03207113 0.2049573 0.02458187 0.001730504 0.03961599 0.0010128952
## 234 234 0.03207138 0.2049481 0.02458204 0.001730713 0.03961909 0.0010130771
## 235 235 0.03207144 0.2049436 0.02458214 0.001730248 0.03960528 0.0010129099
## 236 236 0.03207155 0.2049378 0.02458225 0.001729964 0.03959589 0.0010128528
## 237 237 0.03207166 0.2049333 0.02458232 0.001730128 0.03959893 0.0010132226
## 238 238 0.03207158 0.2049367 0.02458219 0.001730269 0.03960374 0.0010132711
## 239 239 0.03207162 0.2049353 0.02458225 0.001730332 0.03960637 0.0010133297
## 240 240 0.03207168 0.2049328 0.02458231 0.001730399 0.03960843 0.0010134866
## [1] "Best Model"
## nvmax
## 9 9
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## [1] "Coefficients of final model:"
## Estimate 2.5 % 97.5 %
## (Intercept) 1.997430e+00 1.990899e+00 2.003962e+00
## x4 -5.115588e-05 -6.853808e-05 -3.377368e-05
## x7 1.102188e-02 9.794023e-03 1.224974e-02
## x9 3.070804e-03 2.432449e-03 3.709159e-03
## x10 1.278875e-03 6.873502e-04 1.870401e-03
## x16 9.700205e-04 5.568889e-04 1.383152e-03
## x17 1.600779e-03 9.763881e-04 2.225170e-03
## stat98 3.343631e-03 2.875903e-03 3.811359e-03
## stat110 -3.137873e-03 -3.613099e-03 -2.662647e-03
## x18.sqrt 2.631786e-02 2.450088e-02 2.813484e-02
if (algo.backward.caret == TRUE){
test.model(model.backward, data.test
,method = 'leapBackward',subopt = NULL
,formula = formula, feature.names = feature.names, label.names = label.names
,id = id
,draw.limits = TRUE, transformation = t)
}
## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.044 2.084 2.097 2.096 2.108 2.145
## [1] "leapBackward Test MSE: 0.00104102201936567"
if (algo.stepwise.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
,data = data.train
,method = "leapSeq"
,feature.names = feature.names)
model.stepwise = returned$model
id = returned$id
}
## Aggregating results
## Selecting tuning parameters
## Fitting nvmax = 9 on full training set
## [1] "All models results"
## nvmax RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 1 0.03376443 0.1132051 0.02637850 0.001210125 0.02571127 0.0007953495
## 2 2 0.03297241 0.1543836 0.02566825 0.001331813 0.02849647 0.0008195492
## 3 3 0.03250196 0.1779147 0.02515184 0.001317023 0.02808594 0.0007621952
## 4 4 0.03196246 0.2052676 0.02446499 0.001452681 0.03363383 0.0008687720
## 5 5 0.03171086 0.2179498 0.02429750 0.001512147 0.03600988 0.0008518664
## 6 6 0.03165522 0.2206821 0.02425311 0.001516391 0.03578302 0.0008635422
## 7 7 0.03161930 0.2224386 0.02422076 0.001591134 0.03757869 0.0009392440
## 8 8 0.03155244 0.2257309 0.02419734 0.001617014 0.03868599 0.0009624076
## 9 9 0.03146134 0.2301155 0.02411499 0.001613656 0.03869431 0.0009595924
## 10 10 0.03148846 0.2287059 0.02413610 0.001591183 0.03762129 0.0009509402
## 11 11 0.03149049 0.2285003 0.02414479 0.001570434 0.03691604 0.0009354630
## 12 12 0.03150288 0.2280520 0.02416044 0.001590991 0.03717482 0.0009408043
## 13 13 0.03147622 0.2293254 0.02413800 0.001586666 0.03717877 0.0009728358
## 14 14 0.03148550 0.2289291 0.02413604 0.001600811 0.03767695 0.0009991203
## 15 15 0.03151049 0.2277667 0.02415137 0.001606362 0.03779119 0.0009983448
## 16 16 0.03151635 0.2273578 0.02416525 0.001572932 0.03632568 0.0009714183
## 17 17 0.03150438 0.2281246 0.02415982 0.001625619 0.03860212 0.0010191859
## 18 18 0.03150374 0.2280915 0.02415855 0.001606877 0.03802253 0.0009915896
## 19 19 0.03180657 0.2127004 0.02444456 0.001751595 0.05728238 0.0011105427
## 20 20 0.03152427 0.2270617 0.02418562 0.001595441 0.03650130 0.0009624108
## 21 21 0.03185903 0.2103130 0.02448502 0.002082927 0.06575323 0.0014950551
## 22 22 0.03182330 0.2118483 0.02444687 0.001776166 0.05860878 0.0011120743
## 23 23 0.03191553 0.2073860 0.02451267 0.001860581 0.06512860 0.0012336903
## 24 24 0.03216231 0.1944494 0.02463932 0.001641329 0.06674080 0.0011149214
## 25 25 0.03191805 0.2073050 0.02448142 0.001866018 0.06541768 0.0012364730
## 26 26 0.03178503 0.2144358 0.02440437 0.002304475 0.07058771 0.0016239364
## 27 27 0.03155685 0.2258517 0.02417755 0.001662713 0.03949810 0.0010084669
## 28 28 0.03250283 0.1774343 0.02491316 0.001775091 0.06989243 0.0012103644
## 29 29 0.03157131 0.2251786 0.02419074 0.001647132 0.03880779 0.0009873490
## 30 30 0.03154970 0.2261906 0.02415013 0.001629981 0.03831819 0.0009900989
## 31 31 0.03208839 0.1989632 0.02462543 0.002303147 0.07922805 0.0016665527
## 32 32 0.03151614 0.2277098 0.02413535 0.001635320 0.03874525 0.0010068959
## 33 33 0.03186205 0.2104133 0.02448265 0.002109339 0.06676413 0.0015193746
## 34 34 0.03152272 0.2274911 0.02414759 0.001641299 0.03917277 0.0009922418
## 35 35 0.03179208 0.2143355 0.02439784 0.002304906 0.07076244 0.0015970393
## 36 36 0.03157140 0.2252646 0.02418163 0.001636398 0.03897661 0.0009514999
## 37 37 0.03157625 0.2250578 0.02417752 0.001630306 0.03895796 0.0009419378
## 38 38 0.03186736 0.2096566 0.02438792 0.001595737 0.05633185 0.0009614105
## 39 39 0.03158770 0.2245021 0.02418861 0.001609478 0.03814285 0.0009410141
## 40 40 0.03158759 0.2245066 0.02417769 0.001612824 0.03837816 0.0009316826
## 41 41 0.03258460 0.1748103 0.02508744 0.002650055 0.09353770 0.0019488649
## 42 42 0.03219798 0.1928427 0.02469541 0.001840846 0.07329750 0.0013418269
## 43 43 0.03199373 0.2040535 0.02451406 0.001811164 0.06361541 0.0012098364
## 44 44 0.03162754 0.2228378 0.02423172 0.001627799 0.03786267 0.0009368672
## 45 45 0.03261552 0.1727649 0.02509820 0.002028939 0.07298912 0.0014640904
## 46 46 0.03164307 0.2222409 0.02424256 0.001646312 0.03900960 0.0009557584
## 47 47 0.03164358 0.2222103 0.02425024 0.001647030 0.03900757 0.0009616797
## 48 48 0.03198305 0.2051883 0.02451700 0.001709891 0.04970771 0.0010665078
## 49 49 0.03165174 0.2218470 0.02425662 0.001626083 0.03799849 0.0009448402
## 50 50 0.03226029 0.1915580 0.02477124 0.002389323 0.08322468 0.0017547306
## 51 51 0.03198749 0.2050767 0.02452486 0.001723179 0.04990481 0.0010724167
## 52 52 0.03199957 0.2039685 0.02452082 0.001794609 0.06288832 0.0013020712
## 53 53 0.03190377 0.2088868 0.02441388 0.002075109 0.06776368 0.0013079782
## 54 54 0.03166918 0.2212550 0.02427401 0.001658404 0.03866582 0.0009790142
## 55 55 0.03168320 0.2206958 0.02428269 0.001672702 0.03926647 0.0009780532
## 56 56 0.03192533 0.2091444 0.02451080 0.002332062 0.07020993 0.0015932784
## 57 57 0.03223547 0.1932815 0.02475608 0.002317976 0.07748192 0.0016013810
## 58 58 0.03240758 0.1841990 0.02485722 0.001820698 0.06445783 0.0012077502
## 59 59 0.03170542 0.2197424 0.02430603 0.001686600 0.03965226 0.0009944636
## 60 60 0.03205408 0.2024083 0.02464228 0.002125017 0.06580672 0.0014781327
## 61 61 0.03172205 0.2190406 0.02431334 0.001681907 0.03959259 0.0009946280
## 62 62 0.03228275 0.1892624 0.02475234 0.001756194 0.06971364 0.0011156835
## 63 63 0.03229511 0.1892865 0.02478744 0.001827147 0.06339599 0.0011415622
## 64 64 0.03196507 0.2062385 0.02446291 0.002009781 0.06403751 0.0012457144
## 65 65 0.03174477 0.2180366 0.02432846 0.001665271 0.03861272 0.0009678730
## 66 66 0.03263041 0.1733851 0.02505179 0.002308430 0.08286378 0.0016260834
## 67 67 0.03178364 0.2163051 0.02436123 0.001661866 0.03809429 0.0009711526
## 68 68 0.03206828 0.2011030 0.02457051 0.001612803 0.05403266 0.0009557886
## 69 69 0.03205619 0.2020661 0.02458725 0.001825042 0.06032267 0.0011363336
## 70 70 0.03178828 0.2161594 0.02435559 0.001639066 0.03728892 0.0009578125
## 71 71 0.03312894 0.1456091 0.02541524 0.002001845 0.08553175 0.0013312429
## 72 72 0.03179932 0.2156327 0.02437590 0.001630931 0.03683612 0.0009334147
## 73 73 0.03179394 0.2158327 0.02436494 0.001614773 0.03606989 0.0009250698
## 74 74 0.03238655 0.1868727 0.02494840 0.002582359 0.08224267 0.0018342461
## 75 75 0.03181196 0.2150635 0.02438655 0.001614466 0.03639353 0.0009293733
## 76 76 0.03248947 0.1811896 0.02498872 0.002053040 0.06534977 0.0013947616
## 77 77 0.03208432 0.2008153 0.02460894 0.001787448 0.05861012 0.0010997670
## 78 78 0.03208034 0.2008222 0.02461636 0.001778544 0.05801537 0.0010731560
## 79 79 0.03209338 0.2005167 0.02460375 0.001791165 0.05858244 0.0010995603
## 80 80 0.03184774 0.2136155 0.02440057 0.001627854 0.03655651 0.0009292682
## 81 81 0.03184270 0.2138395 0.02439748 0.001631264 0.03664300 0.0009271608
## 82 82 0.03209381 0.2019388 0.02463566 0.002303413 0.06792415 0.0015769932
## 83 83 0.03216917 0.1974000 0.02464777 0.001698973 0.04808826 0.0010144116
## 84 84 0.03245766 0.1824340 0.02486979 0.001721112 0.06358055 0.0011418707
## 85 85 0.03186362 0.2129756 0.02440530 0.001620473 0.03582436 0.0009230939
## 86 86 0.03211202 0.2012632 0.02464720 0.002304124 0.06770321 0.0015774051
## 87 87 0.03187583 0.2124513 0.02442006 0.001627270 0.03602309 0.0009293510
## 88 88 0.03246549 0.1820027 0.02498396 0.002129585 0.07292023 0.0014418823
## 89 89 0.03247020 0.1818635 0.02485957 0.002059604 0.07636237 0.0014919372
## 90 90 0.03223502 0.1943281 0.02471180 0.001785260 0.05945780 0.0011451141
## 91 91 0.03255707 0.1784624 0.02502766 0.002076190 0.06626388 0.0014327729
## 92 92 0.03212982 0.1992593 0.02460689 0.002005100 0.06356797 0.0012457591
## 93 93 0.03217219 0.1967780 0.02466662 0.001586315 0.05217334 0.0009411910
## 94 94 0.03216745 0.1977210 0.02466420 0.001618552 0.04793510 0.0010047667
## 95 95 0.03300307 0.1549856 0.02532738 0.002450403 0.09107113 0.0017126603
## 96 96 0.03248309 0.1809914 0.02494945 0.001792042 0.06209878 0.0010819688
## 97 97 0.03267572 0.1706223 0.02502078 0.001855528 0.07286906 0.0011916604
## 98 98 0.03242779 0.1840332 0.02487291 0.001739959 0.06302466 0.0011061861
## 99 99 0.03194607 0.2094921 0.02450579 0.001639222 0.03611328 0.0009399770
## 100 100 0.03194818 0.2093912 0.02451214 0.001644864 0.03632447 0.0009365280
## 101 101 0.03278677 0.1658663 0.02517803 0.002252411 0.08237153 0.0015313185
## 102 102 0.03195446 0.2092055 0.02451481 0.001657493 0.03674994 0.0009411005
## 103 103 0.03277694 0.1677600 0.02517840 0.002546771 0.09011683 0.0018986587
## 104 104 0.03226725 0.1931580 0.02475257 0.001720810 0.04884957 0.0010216540
## 105 105 0.03278503 0.1674423 0.02519923 0.002279650 0.08097792 0.0017560378
## 106 106 0.03218458 0.1964331 0.02472214 0.001799898 0.05793981 0.0010723418
## 107 107 0.03256156 0.1783155 0.02496798 0.001791113 0.06563365 0.0011764135
## 108 108 0.03347622 0.1311616 0.02572012 0.002059386 0.07824063 0.0015459613
## 109 109 0.03195263 0.2094592 0.02450485 0.001688301 0.03802164 0.0009730070
## 110 110 0.03219052 0.1981661 0.02474483 0.002318487 0.06760490 0.0016053914
## 111 111 0.03252334 0.1797951 0.02502890 0.002171106 0.07414936 0.0014721942
## 112 112 0.03221920 0.1956201 0.02469888 0.001673665 0.05038465 0.0010362436
## 113 113 0.03245085 0.1826447 0.02492555 0.001927148 0.07159623 0.0011925284
## 114 114 0.03219614 0.1961095 0.02472756 0.001815862 0.05818269 0.0010889246
## 115 115 0.03219454 0.1962164 0.02472537 0.001821613 0.05832753 0.0010923521
## 116 116 0.03254807 0.1787824 0.02496456 0.001855737 0.06436864 0.0011591968
## 117 117 0.03265948 0.1744696 0.02510710 0.002214367 0.07666527 0.0015401452
## 118 118 0.03246544 0.1840424 0.02495805 0.002298860 0.07376498 0.0016149487
## 119 119 0.03197181 0.2087687 0.02452912 0.001682093 0.03736782 0.0009753778
## 120 120 0.03197419 0.2086511 0.02453280 0.001672656 0.03703062 0.0009660818
## 121 121 0.03249295 0.1816352 0.02495147 0.001793204 0.06369034 0.0012480058
## 122 122 0.03243901 0.1846224 0.02488597 0.001984879 0.06641123 0.0012887717
## 123 123 0.03257969 0.1782496 0.02499821 0.001781955 0.06345946 0.0013035261
## 124 124 0.03215771 0.1995279 0.02468615 0.001624937 0.04081956 0.0009808812
## 125 125 0.03199166 0.2079617 0.02454281 0.001681791 0.03746445 0.0009744060
## 126 126 0.03259946 0.1774491 0.02501612 0.001789480 0.06352400 0.0012988877
## 127 127 0.03257950 0.1786850 0.02506272 0.002008896 0.06557183 0.0015250913
## 128 128 0.03199860 0.2076612 0.02454475 0.001680452 0.03738761 0.0009771339
## 129 129 0.03200553 0.2074243 0.02454265 0.001693590 0.03787085 0.0009830174
## 130 130 0.03237673 0.1892822 0.02490867 0.002197071 0.06478141 0.0015544970
## 131 131 0.03277095 0.1671905 0.02517120 0.001685743 0.06745602 0.0011780545
## 132 132 0.03200011 0.2077163 0.02453862 0.001702624 0.03822628 0.0009891626
## 133 133 0.03219649 0.1979206 0.02469256 0.001654623 0.03657975 0.0009397937
## 134 134 0.03200920 0.2073912 0.02454764 0.001716740 0.03869600 0.0009939137
## 135 135 0.03219794 0.1989377 0.02473962 0.002230471 0.06132236 0.0015091257
## 136 136 0.03232750 0.1904389 0.02479058 0.001930337 0.05960302 0.0012036057
## 137 137 0.03227318 0.1942744 0.02476719 0.001779307 0.05105972 0.0010981336
## 138 138 0.03284642 0.1648920 0.02516725 0.001620340 0.05606680 0.0011486641
## 139 139 0.03217182 0.1983762 0.02470763 0.001764266 0.04864377 0.0010315767
## 140 140 0.03222010 0.1969888 0.02471311 0.001673310 0.03731038 0.0009548168
## 141 141 0.03203115 0.2064620 0.02456672 0.001721914 0.03915652 0.0009991486
## 142 142 0.03254022 0.1812317 0.02499340 0.002274078 0.06577468 0.0015342045
## 143 143 0.03216936 0.1994328 0.02465016 0.001666891 0.04028133 0.0009878448
## 144 144 0.03203303 0.2064550 0.02456672 0.001733601 0.03956503 0.0010130549
## 145 145 0.03216576 0.1995329 0.02464865 0.001659829 0.04008492 0.0009840849
## 146 146 0.03234594 0.1906656 0.02488200 0.002254655 0.06646640 0.0015102680
## 147 147 0.03203257 0.2064462 0.02456749 0.001726234 0.03930241 0.0010109550
## 148 148 0.03277555 0.1701133 0.02519636 0.002235118 0.06151733 0.0015331982
## 149 149 0.03203933 0.2061971 0.02457127 0.001729333 0.03941595 0.0010133406
## 150 150 0.03252878 0.1818670 0.02500250 0.001988737 0.05969030 0.0013050212
## 151 151 0.03231986 0.1912536 0.02475953 0.001839744 0.05277372 0.0011442123
## 152 152 0.03270099 0.1726110 0.02508621 0.001586663 0.04943492 0.0009465519
## 153 153 0.03279616 0.1682314 0.02521524 0.002403424 0.07547047 0.0016466003
## 154 154 0.03204793 0.2058146 0.02457397 0.001728257 0.03930793 0.0010136622
## 155 155 0.03252093 0.1803958 0.02496550 0.001864033 0.05553328 0.0011233377
## 156 156 0.03204863 0.2057925 0.02457229 0.001730239 0.03938558 0.0010079784
## 157 157 0.03205065 0.2057295 0.02457438 0.001734087 0.03954065 0.0010090151
## 158 158 0.03224639 0.1956403 0.02473041 0.001803532 0.05167764 0.0010886356
## 159 159 0.03227897 0.1943842 0.02478841 0.001967456 0.05259696 0.0012494877
## 160 160 0.03243858 0.1857693 0.02488078 0.001949541 0.06107178 0.0012413248
## 161 161 0.03205295 0.2056610 0.02457585 0.001733653 0.03950760 0.0010093216
## 162 162 0.03205590 0.2055592 0.02457841 0.001738022 0.03963933 0.0010107676
## 163 163 0.03206084 0.2053693 0.02458082 0.001742692 0.03974019 0.0010066030
## 164 164 0.03225325 0.1971671 0.02476619 0.002283092 0.06228799 0.0015367419
## 165 165 0.03231614 0.1926420 0.02479039 0.001809921 0.05235767 0.0011203866
## 166 166 0.03246592 0.1844695 0.02488341 0.001585056 0.04394090 0.0008941183
## 167 167 0.03205903 0.2053964 0.02458083 0.001735062 0.03962292 0.0010076302
## 168 168 0.03251831 0.1823926 0.02495957 0.001849592 0.05998440 0.0011759527
## 169 169 0.03239734 0.1881578 0.02482491 0.001608404 0.03774759 0.0009333947
## 170 170 0.03222165 0.1963218 0.02474366 0.001802611 0.05136022 0.0010681783
## 171 171 0.03206131 0.2053458 0.02457973 0.001742161 0.03998391 0.0010115774
## 172 172 0.03228037 0.1938016 0.02474501 0.001678570 0.04933575 0.0009755835
## 173 173 0.03225715 0.1953247 0.02474400 0.001809714 0.05180095 0.0011032219
## 174 174 0.03249471 0.1828016 0.02495828 0.001791054 0.05808263 0.0012106012
## 175 175 0.03229939 0.1936205 0.02479921 0.001986360 0.05339896 0.0012528897
## 176 176 0.03240468 0.1892697 0.02487375 0.002433367 0.07169875 0.0016487235
## 177 177 0.03206516 0.2051777 0.02458373 0.001746388 0.04016510 0.0010142570
## 178 178 0.03206690 0.2050950 0.02458418 0.001746059 0.04020591 0.0010140861
## 179 179 0.03220469 0.1976533 0.02467090 0.001924977 0.05386313 0.0011476952
## 180 180 0.03206854 0.2050462 0.02458585 0.001747283 0.04028451 0.0010137099
## 181 181 0.03232535 0.1922188 0.02478443 0.001752774 0.05032878 0.0011810224
## 182 182 0.03206500 0.2051892 0.02458547 0.001743100 0.04014883 0.0010145327
## 183 183 0.03232765 0.1921171 0.02478468 0.001749040 0.05030386 0.0011837940
## 184 184 0.03206652 0.2051432 0.02458384 0.001742172 0.04007395 0.0010134162
## 185 185 0.03234190 0.1917588 0.02481271 0.001830687 0.05387810 0.0011521150
## 186 186 0.03227329 0.1967692 0.02478257 0.002317780 0.06271779 0.0015669544
## 187 187 0.03206462 0.2052230 0.02457848 0.001738596 0.03992543 0.0010106557
## 188 188 0.03232442 0.1922840 0.02477902 0.001750168 0.05040209 0.0011869352
## 189 189 0.03206730 0.2051053 0.02458020 0.001741748 0.04005787 0.0010148205
## 190 190 0.03268609 0.1740963 0.02505727 0.001904002 0.05883026 0.0011996750
## 191 191 0.03206811 0.2050694 0.02458214 0.001743898 0.04008077 0.0010127574
## 192 192 0.03207025 0.2049907 0.02458290 0.001744863 0.04009111 0.0010145145
## 193 193 0.03226731 0.1951171 0.02473239 0.001692544 0.03829879 0.0009779075
## 194 194 0.03222126 0.1970422 0.02467817 0.001950298 0.05525669 0.0011745391
## 195 195 0.03206803 0.2050948 0.02457807 0.001743314 0.04006339 0.0010159525
## 196 196 0.03235885 0.1911123 0.02482214 0.001840942 0.05463615 0.0011672515
## 197 197 0.03235678 0.1912217 0.02482040 0.001842818 0.05465493 0.0011682310
## 198 198 0.03271584 0.1719899 0.02510708 0.001697437 0.05321777 0.0011344318
## 199 199 0.03206995 0.2050216 0.02458109 0.001746296 0.04016722 0.0010193117
## 200 200 0.03206855 0.2050847 0.02457934 0.001748313 0.04027412 0.0010197175
## 201 201 0.03206861 0.2050848 0.02457943 0.001748213 0.04022911 0.0010208412
## 202 202 0.03224647 0.1954237 0.02474958 0.001826542 0.05292968 0.0010892217
## 203 203 0.03254725 0.1813046 0.02496030 0.001801565 0.05885501 0.0012624593
## 204 204 0.03206770 0.2051181 0.02457536 0.001745263 0.04015378 0.0010182995
## 205 205 0.03206632 0.2051692 0.02457445 0.001742740 0.04006480 0.0010177920
## 206 206 0.03206777 0.2051166 0.02457590 0.001743580 0.04009384 0.0010194146
## 207 207 0.03206837 0.2050758 0.02457590 0.001741224 0.04001211 0.0010176408
## 208 208 0.03206968 0.2050207 0.02457615 0.001739870 0.03996805 0.0010155763
## 209 209 0.03206953 0.2050276 0.02457688 0.001738998 0.03991646 0.0010149879
## 210 210 0.03225028 0.1952557 0.02475096 0.001818533 0.05277656 0.0010845038
## 211 211 0.03207051 0.2049941 0.02457788 0.001736662 0.03982307 0.0010140456
## 212 212 0.03243601 0.1863240 0.02485060 0.001611372 0.03934622 0.0009440440
## 213 213 0.03207192 0.2049312 0.02457959 0.001734728 0.03977390 0.0010133716
## 214 214 0.03223183 0.1965386 0.02468944 0.001680874 0.04282380 0.0009941573
## 215 215 0.03207362 0.2048447 0.02458269 0.001731383 0.03964952 0.0010114171
## 216 216 0.03273763 0.1719632 0.02515936 0.001930451 0.05571995 0.0012589511
## 217 217 0.03207360 0.2048493 0.02458291 0.001730862 0.03962953 0.0010117337
## 218 218 0.03207367 0.2048519 0.02458347 0.001732159 0.03967375 0.0010137218
## 219 219 0.03235576 0.1909350 0.02478746 0.001760052 0.05222916 0.0012001769
## 220 220 0.03227708 0.1947009 0.02475990 0.001801636 0.05148695 0.0011190900
## 221 221 0.03207300 0.2048841 0.02458170 0.001731904 0.03966357 0.0010147819
## 222 222 0.03230902 0.1927392 0.02476008 0.001671419 0.05003771 0.0009861776
## 223 223 0.03207242 0.2049032 0.02458086 0.001732350 0.03968642 0.0010157095
## 224 224 0.03207233 0.2049031 0.02458054 0.001731883 0.03966506 0.0010149805
## 225 225 0.03227920 0.1946185 0.02476111 0.001804842 0.05173172 0.0011225555
## 226 226 0.03207187 0.2049254 0.02458114 0.001731322 0.03964074 0.0010143681
## 227 227 0.03207190 0.2049216 0.02458136 0.001730803 0.03962087 0.0010141621
## 228 228 0.03207191 0.2049236 0.02458172 0.001730910 0.03963172 0.0010141598
## 229 229 0.03207167 0.2049328 0.02458197 0.001730707 0.03962512 0.0010136789
## 230 230 0.03230080 0.1960977 0.02479123 0.002369198 0.06353051 0.0015907885
## 231 231 0.03231540 0.1930192 0.02481303 0.001976288 0.05295142 0.0012767256
## 232 232 0.03207141 0.2049454 0.02458210 0.001730423 0.03961255 0.0010130997
## 233 233 0.03207113 0.2049573 0.02458187 0.001730504 0.03961599 0.0010128952
## 234 234 0.03260853 0.1782309 0.02497782 0.001663699 0.05826799 0.0011485919
## 235 235 0.03227027 0.1945174 0.02477004 0.001828469 0.05397957 0.0010990078
## 236 236 0.03228877 0.1940785 0.02475450 0.001688007 0.03919501 0.0009894918
## 237 237 0.03315800 0.1499859 0.02548972 0.001657879 0.05323616 0.0010000809
## 238 238 0.03365107 0.1256566 0.02588090 0.001340379 0.04268967 0.0008880158
## 239 239 0.03301288 0.1606469 0.02538267 0.002313877 0.07044983 0.0016553371
## 240 240 0.03207168 0.2049328 0.02458231 0.001730399 0.03960843 0.0010134866
## [1] "Best Model"
## nvmax
## 9 9
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## [1] "Coefficients of final model:"
## Estimate 2.5 % 97.5 %
## (Intercept) 1.997430e+00 1.990899e+00 2.003962e+00
## x4 -5.115588e-05 -6.853808e-05 -3.377368e-05
## x7 1.102188e-02 9.794023e-03 1.224974e-02
## x9 3.070804e-03 2.432449e-03 3.709159e-03
## x10 1.278875e-03 6.873502e-04 1.870401e-03
## x16 9.700205e-04 5.568889e-04 1.383152e-03
## x17 1.600779e-03 9.763881e-04 2.225170e-03
## stat98 3.343631e-03 2.875903e-03 3.811359e-03
## stat110 -3.137873e-03 -3.613099e-03 -2.662647e-03
## x18.sqrt 2.631786e-02 2.450088e-02 2.813484e-02
if (algo.stepwise.caret == TRUE){
test.model(model.stepwise, data.test
,method = 'leapSeq',subopt = NULL
,formula = formula, feature.names = feature.names, label.names = label.names
,id = id
,draw.limits = TRUE, transformation = t)
}
## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.044 2.084 2.097 2.096 2.108 2.145
## [1] "leapSeq Test MSE: 0.00104102201936567"
if (algo.LASSO.caret == TRUE){
set.seed(1)
tune.grid= expand.grid(alpha = 1,lambda = 10^seq(from=-4,to=0,length=100))
returned = train.caret.glmselect(formula = formula
,data = data.train
,method = "glmnet"
,subopt = 'LASSO'
,tune.grid = tune.grid
,feature.names = feature.names)
model.LASSO.caret = returned$model
}
## Warning in nominalTrainWorkflow(x = x, y = y, wts = weights, info = trainInfo, : There were missing values in resampled
## performance measures.
## Aggregating results
## Selecting tuning parameters
## Fitting alpha = 1, lambda = 0.000534 on full training set
## glmnet
##
## 5584 samples
## 240 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 5026, 5026, 5026, 5025, 5025, 5026, ...
## Resampling results across tuning parameters:
##
## lambda RMSE Rsquared MAE
## 0.0001000000 0.03182870 0.2137076 0.02441023
## 0.0001097499 0.03180927 0.2144604 0.02439658
## 0.0001204504 0.03178873 0.2152657 0.02438212
## 0.0001321941 0.03176718 0.2161211 0.02436676
## 0.0001450829 0.03174469 0.2170260 0.02435083
## 0.0001592283 0.03172105 0.2179927 0.02433422
## 0.0001747528 0.03169627 0.2190254 0.02431677
## 0.0001917910 0.03167103 0.2200965 0.02429872
## 0.0002104904 0.03164552 0.2212024 0.02428038
## 0.0002310130 0.03161944 0.2223626 0.02426193
## 0.0002535364 0.03159361 0.2235431 0.02424387
## 0.0002782559 0.03156877 0.2247131 0.02422727
## 0.0003053856 0.03154558 0.2258456 0.02421276
## 0.0003351603 0.03152471 0.2269062 0.02419982
## 0.0003678380 0.03150698 0.2278516 0.02418917
## 0.0004037017 0.03149331 0.2286417 0.02418283
## 0.0004430621 0.03148344 0.2292964 0.02418039
## 0.0004862602 0.03147724 0.2298251 0.02418196
## 0.0005336699 0.03147529 0.2301977 0.02418786
## 0.0005857021 0.03147903 0.2303349 0.02419858
## 0.0006428073 0.03148930 0.2301906 0.02421507
## 0.0007054802 0.03150530 0.2298123 0.02423585
## 0.0007742637 0.03152577 0.2292579 0.02426172
## 0.0008497534 0.03154991 0.2285769 0.02429172
## 0.0009326033 0.03157678 0.2278436 0.02432303
## 0.0010235310 0.03160721 0.2270216 0.02435577
## 0.0011233240 0.03164458 0.2259205 0.02439543
## 0.0012328467 0.03168793 0.2246032 0.02444073
## 0.0013530478 0.03173511 0.2232133 0.02449030
## 0.0014849683 0.03178845 0.2216425 0.02454585
## 0.0016297508 0.03185100 0.2197293 0.02460969
## 0.0017886495 0.03192157 0.2175594 0.02468123
## 0.0019630407 0.03199700 0.2153667 0.02475724
## 0.0021544347 0.03207493 0.2133450 0.02483538
## 0.0023644894 0.03215811 0.2114023 0.02491772
## 0.0025950242 0.03225103 0.2093330 0.02500656
## 0.0028480359 0.03235951 0.2067936 0.02510779
## 0.0031257158 0.03248944 0.2033564 0.02522413
## 0.0034304693 0.03264514 0.1986212 0.02535920
## 0.0037649358 0.03282239 0.1927831 0.02551137
## 0.0041320124 0.03300975 0.1867804 0.02567115
## 0.0045348785 0.03321914 0.1795815 0.02584532
## 0.0049770236 0.03346904 0.1689546 0.02604857
## 0.0054622772 0.03375718 0.1540228 0.02627820
## 0.0059948425 0.03402682 0.1400307 0.02648161
## 0.0065793322 0.03425881 0.1296572 0.02664738
## 0.0072208090 0.03449188 0.1185498 0.02680925
## 0.0079248290 0.03468582 0.1132974 0.02693932
## 0.0086974900 0.03487128 0.1132051 0.02706083
## 0.0095454846 0.03509275 0.1132051 0.02720824
## 0.0104761575 0.03535760 0.1132051 0.02738487
## 0.0114975700 0.03567394 0.1132051 0.02759920
## 0.0126185688 0.03582413 NaN 0.02770080
## 0.0138488637 0.03582413 NaN 0.02770080
## 0.0151991108 0.03582413 NaN 0.02770080
## 0.0166810054 0.03582413 NaN 0.02770080
## 0.0183073828 0.03582413 NaN 0.02770080
## 0.0200923300 0.03582413 NaN 0.02770080
## 0.0220513074 0.03582413 NaN 0.02770080
## 0.0242012826 0.03582413 NaN 0.02770080
## 0.0265608778 0.03582413 NaN 0.02770080
## 0.0291505306 0.03582413 NaN 0.02770080
## 0.0319926714 0.03582413 NaN 0.02770080
## 0.0351119173 0.03582413 NaN 0.02770080
## 0.0385352859 0.03582413 NaN 0.02770080
## 0.0422924287 0.03582413 NaN 0.02770080
## 0.0464158883 0.03582413 NaN 0.02770080
## 0.0509413801 0.03582413 NaN 0.02770080
## 0.0559081018 0.03582413 NaN 0.02770080
## 0.0613590727 0.03582413 NaN 0.02770080
## 0.0673415066 0.03582413 NaN 0.02770080
## 0.0739072203 0.03582413 NaN 0.02770080
## 0.0811130831 0.03582413 NaN 0.02770080
## 0.0890215085 0.03582413 NaN 0.02770080
## 0.0977009957 0.03582413 NaN 0.02770080
## 0.1072267222 0.03582413 NaN 0.02770080
## 0.1176811952 0.03582413 NaN 0.02770080
## 0.1291549665 0.03582413 NaN 0.02770080
## 0.1417474163 0.03582413 NaN 0.02770080
## 0.1555676144 0.03582413 NaN 0.02770080
## 0.1707352647 0.03582413 NaN 0.02770080
## 0.1873817423 0.03582413 NaN 0.02770080
## 0.2056512308 0.03582413 NaN 0.02770080
## 0.2257019720 0.03582413 NaN 0.02770080
## 0.2477076356 0.03582413 NaN 0.02770080
## 0.2718588243 0.03582413 NaN 0.02770080
## 0.2983647240 0.03582413 NaN 0.02770080
## 0.3274549163 0.03582413 NaN 0.02770080
## 0.3593813664 0.03582413 NaN 0.02770080
## 0.3944206059 0.03582413 NaN 0.02770080
## 0.4328761281 0.03582413 NaN 0.02770080
## 0.4750810162 0.03582413 NaN 0.02770080
## 0.5214008288 0.03582413 NaN 0.02770080
## 0.5722367659 0.03582413 NaN 0.02770080
## 0.6280291442 0.03582413 NaN 0.02770080
## 0.6892612104 0.03582413 NaN 0.02770080
## 0.7564633276 0.03582413 NaN 0.02770080
## 0.8302175681 0.03582413 NaN 0.02770080
## 0.9111627561 0.03582413 NaN 0.02770080
## 1.0000000000 0.03582413 NaN 0.02770080
##
## Tuning parameter 'alpha' was held constant at a value of 1
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were alpha = 1 and lambda = 0.0005336699.
## alpha lambda
## 19 1 0.0005336699
## alpha lambda RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 1 0.0001000000 0.03182870 0.2137076 0.02441023 0.001693146 0.03945645 0.0009800245
## 2 1 0.0001097499 0.03180927 0.2144604 0.02439658 0.001688426 0.03938261 0.0009767729
## 3 1 0.0001204504 0.03178873 0.2152657 0.02438212 0.001683062 0.03928942 0.0009730537
## 4 1 0.0001321941 0.03176718 0.2161211 0.02436676 0.001677332 0.03918452 0.0009691814
## 5 1 0.0001450829 0.03174469 0.2170260 0.02435083 0.001670837 0.03905908 0.0009654273
## 6 1 0.0001592283 0.03172105 0.2179927 0.02433422 0.001663569 0.03891894 0.0009621797
## 7 1 0.0001747528 0.03169627 0.2190254 0.02431677 0.001655845 0.03877402 0.0009589892
## 8 1 0.0001917910 0.03167103 0.2200965 0.02429872 0.001647780 0.03862923 0.0009555977
## 9 1 0.0002104904 0.03164552 0.2212024 0.02428038 0.001639412 0.03848927 0.0009521441
## 10 1 0.0002310130 0.03161944 0.2223626 0.02426193 0.001631188 0.03837580 0.0009492318
## 11 1 0.0002535364 0.03159361 0.2235431 0.02424387 0.001623645 0.03830226 0.0009470889
## 12 1 0.0002782559 0.03156877 0.2247131 0.02422727 0.001616684 0.03826799 0.0009452206
## 13 1 0.0003053856 0.03154558 0.2258456 0.02421276 0.001610379 0.03829091 0.0009433200
## 14 1 0.0003351603 0.03152471 0.2269062 0.02419982 0.001604161 0.03834123 0.0009413149
## 15 1 0.0003678380 0.03150698 0.2278516 0.02418917 0.001597607 0.03836861 0.0009401939
## 16 1 0.0004037017 0.03149331 0.2286417 0.02418283 0.001590996 0.03837797 0.0009383324
## 17 1 0.0004430621 0.03148344 0.2292964 0.02418039 0.001584576 0.03840897 0.0009361478
## 18 1 0.0004862602 0.03147724 0.2298251 0.02418196 0.001577649 0.03842867 0.0009340461
## 19 1 0.0005336699 0.03147529 0.2301977 0.02418786 0.001569060 0.03835303 0.0009303565
## 20 1 0.0005857021 0.03147903 0.2303349 0.02419858 0.001557618 0.03810712 0.0009237975
## 21 1 0.0006428073 0.03148930 0.2301906 0.02421507 0.001544691 0.03777284 0.0009163365
## 22 1 0.0007054802 0.03150530 0.2298123 0.02423585 0.001533169 0.03753338 0.0009102606
## 23 1 0.0007742637 0.03152577 0.2292579 0.02426172 0.001522240 0.03736032 0.0009035369
## 24 1 0.0008497534 0.03154991 0.2285769 0.02429172 0.001511755 0.03725715 0.0008963947
## 25 1 0.0009326033 0.03157678 0.2278436 0.02432303 0.001501021 0.03720320 0.0008886619
## 26 1 0.0010235310 0.03160721 0.2270216 0.02435577 0.001489218 0.03709465 0.0008798247
## 27 1 0.0011233240 0.03164458 0.2259205 0.02439543 0.001476820 0.03691704 0.0008712574
## 28 1 0.0012328467 0.03168793 0.2246032 0.02444073 0.001464015 0.03675448 0.0008659036
## 29 1 0.0013530478 0.03173511 0.2232133 0.02449030 0.001449634 0.03656470 0.0008614688
## 30 1 0.0014849683 0.03178845 0.2216425 0.02454585 0.001432974 0.03627258 0.0008544587
## 31 1 0.0016297508 0.03185100 0.2197293 0.02460969 0.001413036 0.03580356 0.0008448008
## 32 1 0.0017886495 0.03192157 0.2175594 0.02468123 0.001390078 0.03520147 0.0008328110
## 33 1 0.0019630407 0.03199700 0.2153667 0.02475724 0.001367349 0.03459826 0.0008197790
## 34 1 0.0021544347 0.03207493 0.2133450 0.02483538 0.001347811 0.03407788 0.0008092411
## 35 1 0.0023644894 0.03215811 0.2114023 0.02491772 0.001329824 0.03354756 0.0008015722
## 36 1 0.0025950242 0.03225103 0.2093330 0.02500656 0.001311728 0.03306585 0.0007946204
## 37 1 0.0028480359 0.03235951 0.2067936 0.02510779 0.001292026 0.03253696 0.0007883657
## 38 1 0.0031257158 0.03248944 0.2033564 0.02522413 0.001270512 0.03189223 0.0007813295
## 39 1 0.0034304693 0.03264514 0.1986212 0.02535920 0.001247045 0.03110118 0.0007734591
## 40 1 0.0037649358 0.03282239 0.1927831 0.02551137 0.001224075 0.03047186 0.0007623563
## 41 1 0.0041320124 0.03300975 0.1867804 0.02567115 0.001202377 0.03010563 0.0007491561
## 42 1 0.0045348785 0.03321914 0.1795815 0.02584532 0.001178684 0.02966345 0.0007312001
## 43 1 0.0049770236 0.03346904 0.1689546 0.02604857 0.001153037 0.02932342 0.0007116703
## 44 1 0.0054622772 0.03375718 0.1540228 0.02627820 0.001129102 0.02889451 0.0006960095
## 45 1 0.0059948425 0.03402682 0.1400307 0.02648161 0.001110666 0.02868495 0.0006806742
## 46 1 0.0065793322 0.03425881 0.1296572 0.02664738 0.001090611 0.02792209 0.0006585626
## 47 1 0.0072208090 0.03449188 0.1185498 0.02680925 0.001072559 0.02616045 0.0006385552
## 48 1 0.0079248290 0.03468582 0.1132974 0.02693932 0.001063775 0.02585808 0.0006273047
## 49 1 0.0086974900 0.03487128 0.1132051 0.02706083 0.001052059 0.02571127 0.0006175194
## 50 1 0.0095454846 0.03509275 0.1132051 0.02720824 0.001040454 0.02571127 0.0006101350
## 51 1 0.0104761575 0.03535760 0.1132051 0.02738487 0.001028840 0.02571127 0.0006070960
## 52 1 0.0114975700 0.03567394 0.1132051 0.02759920 0.001017520 0.02571127 0.0006053083
## 53 1 0.0126185688 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 54 1 0.0138488637 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 55 1 0.0151991108 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 56 1 0.0166810054 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 57 1 0.0183073828 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 58 1 0.0200923300 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 59 1 0.0220513074 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 60 1 0.0242012826 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 61 1 0.0265608778 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 62 1 0.0291505306 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 63 1 0.0319926714 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 64 1 0.0351119173 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 65 1 0.0385352859 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 66 1 0.0422924287 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 67 1 0.0464158883 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 68 1 0.0509413801 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 69 1 0.0559081018 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 70 1 0.0613590727 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 71 1 0.0673415066 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 72 1 0.0739072203 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 73 1 0.0811130831 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 74 1 0.0890215085 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 75 1 0.0977009957 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 76 1 0.1072267222 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 77 1 0.1176811952 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 78 1 0.1291549665 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 79 1 0.1417474163 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 80 1 0.1555676144 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 81 1 0.1707352647 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 82 1 0.1873817423 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 83 1 0.2056512308 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 84 1 0.2257019720 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 85 1 0.2477076356 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 86 1 0.2718588243 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 87 1 0.2983647240 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 88 1 0.3274549163 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 89 1 0.3593813664 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 90 1 0.3944206059 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 91 1 0.4328761281 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 92 1 0.4750810162 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 93 1 0.5214008288 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 94 1 0.5722367659 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 95 1 0.6280291442 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 96 1 0.6892612104 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 97 1 0.7564633276 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 98 1 0.8302175681 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 99 1 0.9111627561 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## 100 1 1.0000000000 0.03582413 NaN 0.02770080 0.001017706 NA 0.0006078002
## Warning: Removed 48 rows containing missing values (geom_path).
## Warning: Removed 48 rows containing missing values (geom_point).
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## [1] "Coefficients"
## model.coef
## (Intercept) 1.994914e+00
## x4 -4.002366e-05
## x7 1.024848e-02
## x8 2.632932e-04
## x9 2.657880e-03
## x10 9.133035e-04
## x11 6.455140e+04
## x16 7.020978e-04
## x17 1.191654e-03
## x19 5.520463e-05
## x21 7.165645e-05
## x22 -5.468921e-05
## stat4 -2.637319e-04
## stat5 -7.989719e-05
## stat8 4.810475e-06
## stat10 -2.798960e-05
## stat13 -5.312046e-05
## stat14 -5.253446e-04
## stat15 -1.651295e-04
## stat20 -2.894415e-05
## stat22 -2.008800e-04
## stat23 4.078054e-04
## stat24 -2.411983e-04
## stat25 -1.917754e-04
## stat30 4.191991e-05
## stat35 -1.717092e-04
## stat37 -2.508905e-04
## stat38 2.179254e-04
## stat41 -3.531813e-04
## stat45 -1.414883e-05
## stat54 -9.071240e-05
## stat59 1.036277e-04
## stat60 2.073650e-04
## stat65 -6.888327e-05
## stat82 2.532324e-05
## stat91 -6.976596e-05
## stat92 -4.683807e-05
## stat96 -1.531965e-04
## stat98 3.040515e-03
## stat99 6.912739e-05
## stat100 1.716283e-04
## stat103 -2.060162e-04
## stat106 -7.235702e-05
## stat110 -2.881217e-03
## stat113 -1.179757e-04
## stat118 -1.133401e-04
## stat119 9.665617e-07
## stat121 -4.413637e-06
## stat144 3.607457e-04
## stat146 -3.923816e-05
## stat147 -1.852727e-05
## stat148 -7.355995e-05
## stat149 -1.424650e-04
## stat156 2.644802e-04
## stat164 4.808845e-05
## stat168 -3.883916e-05
## stat195 7.705825e-05
## stat198 -1.183566e-04
## stat204 -2.480254e-04
## stat207 4.379853e-05
## x18.sqrt 2.509646e-02
if (algo.LASSO.caret == TRUE){
test.model(model.LASSO.caret, data.test
,method = 'glmnet',subopt = "LASSO"
,formula = formula, feature.names = feature.names, label.names = label.names
,draw.limits = TRUE, transformation = t)
}
## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.045 2.085 2.097 2.096 2.107 2.141
## [1] "glmnet LASSO Test MSE: 0.00104517306987558"
if (algo.LARS.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
,data = data.train
,method = "lars"
,subopt = 'NULL'
,feature.names = feature.names)
model.LARS.caret = returned$model
}
## Warning in nominalTrainWorkflow(x = x, y = y, wts = weights, info = trainInfo, : There were missing values in resampled
## performance measures.
## Aggregating results
## Selecting tuning parameters
## Fitting fraction = 0.404 on full training set
## Least Angle Regression
##
## 5584 samples
## 240 predictor
##
## Pre-processing: centered (240), scaled (240)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 5026, 5026, 5026, 5025, 5025, 5026, ...
## Resampling results across tuning parameters:
##
## fraction RMSE Rsquared MAE
## 0.00000000 0.03582413 NaN 0.02770080
## 0.01010101 0.03540595 0.1132051 0.02741614
## 0.02020202 0.03503208 0.1132051 0.02716554
## 0.03030303 0.03470397 0.1132051 0.02694770
## 0.04040404 0.03442783 0.1210066 0.02676414
## 0.05050505 0.03417085 0.1334345 0.02658317
## 0.06060606 0.03394463 0.1433609 0.02642105
## 0.07070707 0.03372956 0.1553607 0.02625582
## 0.08080808 0.03352388 0.1664433 0.02609206
## 0.09090909 0.03333009 0.1752792 0.02593508
## 0.10101010 0.03314838 0.1822585 0.02578632
## 0.11111111 0.03297905 0.1877397 0.02564435
## 0.12121212 0.03282549 0.1924615 0.02551380
## 0.13131313 0.03267923 0.1975846 0.02538996
## 0.14141414 0.03254236 0.2018999 0.02527278
## 0.15151515 0.03241552 0.2054266 0.02516078
## 0.16161616 0.03229883 0.2082933 0.02505421
## 0.17171717 0.03219309 0.2106309 0.02495408
## 0.18181818 0.03210235 0.2127016 0.02486571
## 0.19191919 0.03202232 0.2146368 0.02478477
## 0.20202020 0.03194921 0.2167190 0.02471080
## 0.21212121 0.03188044 0.2187742 0.02464139
## 0.22222222 0.03181521 0.2207958 0.02457495
## 0.23232323 0.03175799 0.2225278 0.02451541
## 0.24242424 0.03171064 0.2238902 0.02446561
## 0.25252525 0.03166878 0.2251593 0.02442188
## 0.26262626 0.03163238 0.2262811 0.02438391
## 0.27272727 0.03160361 0.2271049 0.02435351
## 0.28282828 0.03158123 0.2277074 0.02432900
## 0.29292929 0.03156220 0.2282257 0.02430725
## 0.30303030 0.03154560 0.2286958 0.02428701
## 0.31313131 0.03153132 0.2290834 0.02426925
## 0.32323232 0.03151874 0.2294364 0.02425372
## 0.33333333 0.03150815 0.2297192 0.02424055
## 0.34343434 0.03149904 0.2299514 0.02422915
## 0.35353535 0.03149054 0.2301770 0.02421826
## 0.36363636 0.03148428 0.2303104 0.02420917
## 0.37373737 0.03147971 0.2303783 0.02420182
## 0.38383838 0.03147689 0.2303738 0.02419595
## 0.39393939 0.03147600 0.2302808 0.02419190
## 0.40404040 0.03147557 0.2301769 0.02418866
## 0.41414141 0.03147607 0.2300369 0.02418619
## 0.42424242 0.03147741 0.2298669 0.02418400
## 0.43434343 0.03147914 0.2296844 0.02418259
## 0.44444444 0.03148085 0.2295107 0.02418113
## 0.45454545 0.03148324 0.2293129 0.02418058
## 0.46464646 0.03148640 0.2290873 0.02418091
## 0.47474747 0.03149027 0.2288332 0.02418160
## 0.48484848 0.03149424 0.2285836 0.02418302
## 0.49494949 0.03149875 0.2283138 0.02418507
## 0.50505051 0.03150418 0.2280050 0.02418785
## 0.51515152 0.03151039 0.2276631 0.02419141
## 0.52525253 0.03151728 0.2272942 0.02419569
## 0.53535354 0.03152455 0.2269138 0.02420033
## 0.54545455 0.03153195 0.2265324 0.02420515
## 0.55555556 0.03153998 0.2261271 0.02421026
## 0.56565657 0.03154869 0.2256931 0.02421572
## 0.57575758 0.03155724 0.2252730 0.02422098
## 0.58585859 0.03156620 0.2248398 0.02422660
## 0.59595960 0.03157543 0.2243990 0.02423244
## 0.60606061 0.03158494 0.2239508 0.02423867
## 0.61616162 0.03159473 0.2234949 0.02424538
## 0.62626263 0.03160487 0.2230269 0.02425251
## 0.63636364 0.03161523 0.2225546 0.02425977
## 0.64646465 0.03162553 0.2220903 0.02426695
## 0.65656566 0.03163604 0.2216219 0.02427441
## 0.66666667 0.03164682 0.2211470 0.02428211
## 0.67676768 0.03165759 0.2206775 0.02428968
## 0.68686869 0.03166844 0.2202084 0.02429735
## 0.69696970 0.03167956 0.2197316 0.02430527
## 0.70707071 0.03169082 0.2192540 0.02431321
## 0.71717172 0.03170235 0.2187690 0.02432144
## 0.72727273 0.03171414 0.2182764 0.02432963
## 0.73737374 0.03172599 0.2177857 0.02433783
## 0.74747475 0.03173779 0.2173025 0.02434609
## 0.75757576 0.03174967 0.2168209 0.02435432
## 0.76767677 0.03176159 0.2163421 0.02436268
## 0.77777778 0.03177379 0.2158555 0.02437139
## 0.78787879 0.03178607 0.2153697 0.02438020
## 0.79797980 0.03179849 0.2148808 0.02438895
## 0.80808081 0.03181113 0.2143863 0.02439782
## 0.81818182 0.03182379 0.2138953 0.02440678
## 0.82828283 0.03183650 0.2134065 0.02441560
## 0.83838384 0.03184946 0.2129117 0.02442461
## 0.84848485 0.03186265 0.2124109 0.02443386
## 0.85858586 0.03187583 0.2119155 0.02444299
## 0.86868687 0.03188914 0.2114178 0.02445240
## 0.87878788 0.03190257 0.2109196 0.02446203
## 0.88888889 0.03191625 0.2104145 0.02447182
## 0.89898990 0.03193014 0.2099052 0.02448164
## 0.90909091 0.03194389 0.2094070 0.02449128
## 0.91919192 0.03195769 0.2089116 0.02450091
## 0.92929293 0.03197160 0.2084148 0.02451068
## 0.93939394 0.03198565 0.2079157 0.02452050
## 0.94949495 0.03199982 0.2074155 0.02453046
## 0.95959596 0.03201395 0.2069219 0.02454039
## 0.96969697 0.03202814 0.2064297 0.02455073
## 0.97979798 0.03204240 0.2059379 0.02456118
## 0.98989899 0.03205687 0.2054404 0.02457160
## 1.00000000 0.03207168 0.2049328 0.02458231
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was fraction = 0.4040404.
## fraction
## 41 0.4040404
## Warning: Removed 1 rows containing missing values (geom_point).
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## [1] "Coefficients"
## x4 x7 x8 x9 x10 x11 x16 x17
## -1.895935e-03 6.888954e-03 7.569258e-04 3.434031e-03 1.269481e-03 3.676435e-04 1.398042e-03 1.569943e-03
## x19 x21 x22 stat4 stat5 stat10 stat13 stat14
## 1.345776e-04 7.218064e-04 -6.144920e-05 -4.475185e-04 -1.338374e-04 -4.190862e-05 -8.605246e-05 -9.037538e-04
## stat15 stat20 stat22 stat23 stat24 stat25 stat30 stat35
## -2.823696e-04 -4.370507e-05 -3.404304e-04 7.018155e-04 -4.102895e-04 -3.264800e-04 6.587527e-05 -2.895053e-04
## stat37 stat38 stat41 stat45 stat54 stat59 stat60 stat65
## -4.231346e-04 3.686324e-04 -6.099668e-04 -1.833645e-05 -1.486452e-04 1.732624e-04 3.504797e-04 -1.121047e-04
## stat82 stat91 stat92 stat96 stat98 stat99 stat100 stat103
## 3.725948e-05 -1.154440e-04 -7.436628e-05 -2.585713e-04 5.365784e-03 1.121694e-04 2.896916e-04 -3.438299e-04
## stat106 stat110 stat113 stat118 stat144 stat146 stat147 stat148
## -1.197480e-04 -5.001610e-03 -1.969201e-04 -1.902694e-04 6.195373e-04 -6.053854e-05 -2.531191e-05 -1.216201e-04
## stat149 stat156 stat164 stat168 stat195 stat198 stat204 stat207
## -2.378832e-04 4.447563e-04 7.603393e-05 -6.001526e-05 1.258098e-04 -1.978183e-04 -4.247122e-04 6.878251e-05
## x18.sqrt
## 1.140877e-02
if (algo.LARS.caret == TRUE){
test.model(model.LARS.caret, data.test
,method = 'lars',subopt = NULL
,formula = formula, feature.names = feature.names, label.names = label.names
,draw.limits = TRUE, transformation = t)
}
## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.045 2.085 2.097 2.096 2.107 2.141
## [1] "lars Test MSE: 0.00104526315244053"
sessionInfo()
## R version 3.5.2 (2018-12-20)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 17763)
##
## Matrix products: default
##
## locale:
## [1] LC_COLLATE=English_United States.1252 LC_CTYPE=English_United States.1252 LC_MONETARY=English_United States.1252
## [4] LC_NUMERIC=C LC_TIME=English_United States.1252
##
## attached base packages:
## [1] parallel stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] knitr_1.21 htmltools_0.3.6 reshape2_1.4.3 lars_1.2
## [5] doParallel_1.0.14 iterators_1.0.10 caret_6.0-81 leaps_3.0
## [9] ggforce_0.1.3 rlist_0.4.6.1 car_3.0-2 carData_3.0-2
## [13] bestNormalize_1.3.0 scales_1.0.0 onewaytests_2.0 caTools_1.17.1.1
## [17] mosaic_1.5.0 mosaicData_0.17.0 ggformula_0.9.1 ggstance_0.3.1
## [21] lattice_0.20-38 DT_0.5 ggiraphExtra_0.2.9 ggiraph_0.6.0
## [25] investr_1.4.0 glmnet_2.0-16 foreach_1.4.4 Matrix_1.2-15
## [29] MASS_7.3-51.1 PerformanceAnalytics_1.5.2 xts_0.11-2 zoo_1.8-4
## [33] forcats_0.3.0 stringr_1.4.0 dplyr_0.8.0.1 purrr_0.3.0
## [37] readr_1.3.1 tidyr_0.8.2 tibble_2.0.1 ggplot2_3.1.0
## [41] tidyverse_1.2.1 usdm_1.1-18 raster_2.8-19 sp_1.3-1
## [45] pacman_0.5.0
##
## loaded via a namespace (and not attached):
## [1] readxl_1.3.0 backports_1.1.3 plyr_1.8.4 lazyeval_0.2.1 splines_3.5.2 mycor_0.1.1
## [7] crosstalk_1.0.0 leaflet_2.0.2 digest_0.6.18 magrittr_1.5 mosaicCore_0.6.0 openxlsx_4.1.0
## [13] recipes_0.1.4 modelr_0.1.3 gower_0.1.2 colorspace_1.4-0 rvest_0.3.2 ggrepel_0.8.0
## [19] haven_2.0.0 xfun_0.4 crayon_1.3.4 jsonlite_1.6 survival_2.43-3 glue_1.3.0
## [25] registry_0.5 gtable_0.2.0 ppcor_1.1 ipred_0.9-8 sjmisc_2.7.7 abind_1.4-5
## [31] rngtools_1.3.1 bibtex_0.4.2 Rcpp_1.0.0 xtable_1.8-3 units_0.6-2 foreign_0.8-71
## [37] stats4_3.5.2 lava_1.6.5 prodlim_2018.04.18 prediction_0.3.6.2 htmlwidgets_1.3 httr_1.4.0
## [43] RColorBrewer_1.1-2 pkgconfig_2.0.2 farver_1.1.0 nnet_7.3-12 labeling_0.3 tidyselect_0.2.5
## [49] rlang_0.3.1 later_0.8.0 munsell_0.5.0 cellranger_1.1.0 tools_3.5.2 cli_1.0.1
## [55] generics_0.0.2 moments_0.14 sjlabelled_1.0.16 broom_0.5.1 evaluate_0.13 ggdendro_0.1-20
## [61] yaml_2.2.0 ModelMetrics_1.2.2 zip_1.0.0 nlme_3.1-137 doRNG_1.7.1 mime_0.6
## [67] xml2_1.2.0 compiler_3.5.2 rstudioapi_0.9.0 curl_3.3 tweenr_1.0.1 stringi_1.3.1
## [73] highr_0.7 gdtools_0.1.7 stringdist_0.9.5.1 pillar_1.3.1 data.table_1.12.0 bitops_1.0-6
## [79] httpuv_1.4.5.1 R6_2.4.0 promises_1.0.1 gridExtra_2.3 rio_0.5.16 codetools_0.2-15
## [85] assertthat_0.2.0 pkgmaker_0.27 withr_2.1.2 nortest_1.0-4 mgcv_1.8-26 hms_0.4.2
## [91] quadprog_1.5-5 grid_3.5.2 rpart_4.1-13 timeDate_3043.102 class_7.3-14 rmarkdown_1.11
## [97] snakecase_0.9.2 shiny_1.2.0 lubridate_1.7.4